Bs Project Grp 8

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Institute of Management Technology, Ghaziabad

Project Report

On

Investment in Retirement

Submitted as the Term 1 project for Business Statistics

for the session 2011-2012

Submitted to : Dr. Roma Mitra

Date of Submission : 6 September 2011

Submitted By:GROUP - 8, SECTION – B

Ankit Gupta - 11IB-008 International Business

Hitesh Kothari - 11IB-025 International Business

Mohit Jain - 11DM-073 Marketing

Pallavi Kumar - 11DM-098 Marketing

Roby Babu - 11IT-027 Information Technology

Soumyarup Chatterjee - 11FN-106 Finance



Group 8 – Investment on Retirement 2

PAGE INDEX

Topic Page No.

1. INTRODUCTION : THE CASE 3

2. OBJECTIVES 4

3. METHODOLOGY

USED

5

4. ANALYSIS

4.1 CASE DATA

4.2 PROBLEM FORMULATION

4.3 SCATTER PLOT ANALYSIS

4.4 CORRELATION ANALYSIS

4.5 REGRESSION ANALYSIS

4.6 RESIDUAL PLOTS & NORMAL

PROBABILITY CURVE

6

6

10

10

12

14

25

5. CONCLUSION 28

6. MANAGERIAL INPLICATIONS 29




SECTION – 1 INTRODUCTION : THE CASE

1.1 Problem Statement :

Financial advisors offer many types of advice to customers, but they generally agree that one of the

best things people can do is invest as much as possible in tax-deferred retirement plans. Not only

are the earnings from these investments exempt from income tax (until retirement), but the in-

vestment itself is tax-exempt. This means that if a person invests, say, $10,000 income of his

$100,000 income a tax-deferred retirement plan, he pays in-come tax that year on only $90,000 of

his income. This is probably the best method available to most people for avoiding tax payments.

However, which group takes advantage of this attractive investment opportunity: everyone, people

with low salaries, people with high salaries, or who?

The file RETIREPLAN.XLS lets you investigate this question. It contains data on 194 couples:

number of dependent children, combined annual salary of husband and wife, current mortgage on

home, aver-age amount of other (nonmortgage) debt, and percentage of combined income invested

in tax-deferred retirement plans (assumed to be limited to 15%, which is realistic). Using

correlations, scatter-plots, and regression analysis, what can you conclude about the tendency to

invest in tax-deferred retirement plans in this group of people?




SECTION – 2 OBJECTIVES

2.1 OBJECTIVES:

To take suitable managerial decisions about the tendency to invest in tax deferred retirement plan

from group of 194 couples depending on their number of dependent children, combined annual

salary of husband and wife, current mortage on home and other debt using correlation, scatterplot

and regression analysis.




SECTION – 3 METHODOLOGY USED

3.1 METHODOLOGY USED :

1) Scatterplots

2) Correlation Analysis

3) Multiple Regression

4) Hypothesis Testing

5) Study of ANOVA table.

6) Study of residual plot and normal probability plot




SECTION – 4 ANALYSIS

4.1 CASE DATA

In the given excel sheet we are provided with the following data.

Amounts invested in tax-deferred retirement plans

Couple Children Salary Mortgage Debt Invested Invested amount1 2 95920 87340 6230 6.0% 5755.22 3 99850 105320 15240 9.9% 9885.153 1 81940 35720 2030 9.0% 7374.64 2 70370 78610 13450 8.4% 5911.085 1 77430 55640 5270 15.0% 11614.56 4 55090 130020 11260 0.0% 07 2 89730 99600 11520 4.8% 4307.048 2 58330 85320 10630 2.9% 1691.579 3 50730 102220 11740 0.0% 0

10 3 65760 114050 19380 9.5% 6247.211 0 100820 76250 9140 9.7% 9779.5412 2 48310 39840 3260 3.6% 1739.1613 2 44690 47760 9880 9.4% 4200.86

14 2 76120 35650 9370 8.4% 6394.0815 3 32120 65560 10500 7.5% 240916 2 110950 120710 16970 15.0% 16642.517 2 61180 68890 6650 8.8% 5383.8418 2 100290 104540 19480 3.9% 3911.3119 0 43810 39540 7850 15.0% 6571.520 1 73320 75800 5980 6.8% 4985.7621 1 103070 103040 3010 15.0% 15460.522 3 71960 67280 12800 4.7% 3382.1223 1 87170 83130 14940 10.1% 8804.1724 2 71700 59920 6930 13.9% 9966.3

25 1 110580 94030 8230 11.8% 13048.4426 3 86930 103450 13600 14.0% 12170.227 1 57620 50980 5130 5.8% 3341.9628 1 54420 54850 10590 0.0% 029 1 100450 75050 15790 5.3% 5323.8530 2 39680 72590 15810 4.5% 1785.631 1 97360 76020 13180 7.6% 7399.3632 3 53050 76390 16870 0.0% 033 2 82760 47790 16490 10.6% 8772.5634 2 53780 100470 18740 0.0% 035 0 52180 75910 5880 8.2% 4278.76

36 3 58240 96630 14220 11.4% 6639.3637 2 68480 83230 1240 5.3% 3629.4438 3 98060 124960 11630 7.2% 7060.32




39 0 89470 77950 4630 13.6% 12167.9240 2 128230 143480 20620 5.7% 7309.1141 4 77470 128690 23670 0.0% 042 2 85390 94010 4050 10.4% 8880.5643 1 60130 70270 4520 7.5% 4509.75

44 3 90090 114130 8390 7.5% 6756.7545 1 74660 56740 16160 7.0% 5226.246 1 90970 101050 3310 8.2% 7459.5447 2 62450 44200 11100 11.7% 7306.6548 3 89760 137030 17120 0.0% 049 1 68600 113640 7100 1.4% 960.450 2 75040 92510 13100 4.4% 3301.7651 3 38310 23760 12360 5.2% 1992.1252 3 72330 69200 10210 12.6% 9113.5853 2 97680 94650 9670 10.5% 10256.454 3 49810 71860 8900 5.7% 2839.1755 3 73420 149560 20940 0.0% 056 3 63030 85950 3530 12.0% 7563.657 3 46410 73330 13830 1.5% 696.1558 2 51280 51240 9250 4.2% 2153.7659 0 78970 51290 620 12.4% 9792.2860 2 36270 64380 7460 1.5% 544.0561 0 79910 22310 0 9.0% 7191.962 1 36370 20580 8510 4.4% 1600.2863 2 63810 69330 7970 7.3% 4658.1364 3 64110 124480 7820 8.7% 5577.5765 1 90630 82530 17090 4.3% 3897.0966 2 83210 94290 4390 4.7% 3910.8767 1 103280 60610 4210 10.4% 10741.1268 2 71020 80630 13850 8.4% 5965.6869 1 95590 71820 9500 15.0% 14338.570 2 98950 53410 5840 15.0% 14842.571 4 33020 100920 17800 0.0% 072 3 71330 66790 16700 8.5% 6063.0573 2 40380 73450 7430 0.9% 363.4274 2 73020 112630 14080 6.3% 4600.2675 3 63730 93420 14910 0.0% 076 1 96500 99330 12190 10.6% 1022977 2 132060 97140 10910 15.0% 19809

78 1 70160 93190 12430 2.9% 2034.6479 1 72380 86350 2000 6.0% 4342.880 3 45200 99300 6300 0.0% 081 1 86990 100670 12100 1.0% 869.982 3 44620 96890 9850 3.6% 1606.3283 3 90950 110720 14750 10.5% 9549.7584 1 77160 75780 4400 9.4% 7253.0485 2 49140 50760 10230 2.2% 1081.0886 2 62800 102240 7030 0.0% 087 3 35060 46090 9430 5.0% 175388 2 75610 45470 4400 10.6% 8014.66

89 2 54770 89750 1960 7.2% 3943.4490 1 56070 72030 3840 5.2% 2915.6491 1 32640 25460 8060 7.1% 2317.44




92 0 124360 73880 7300 15.0% 1865493 3 84740 98820 15670 1.9% 1610.0694 2 110010 106890 13470 10.3% 11331.0395 2 45490 55330 10780 3.6% 1637.6496 1 121760 120800 8040 14.1% 17168.16

97 0 59240 21840 3090 15.0% 888698 2 64660 21250 0 14.3% 9246.3899 3 90040 120950 9810 6.9% 6212.76

100 2 47740 64370 8800 8.3% 3962.42101 3 83150 132920 15420 2.6% 2161.9102 3 78630 107140 9160 5.0% 3931.5103 3 58160 104090 7830 4.4% 2559.04104 1 82370 82450 12340 15.0% 12355.5105 2 76450 86220 13290 10.2% 7797.9106 3 43060 53570 11410 0.0% 0107 2 83380 83370 3060 15.0% 12507108 3 105510 99530 17210 4.7% 4958.97109 1 59620 18190 9140 8.1% 4829.22110 2 58500 47290 7370 10.1% 5908.5111 2 44220 84250 13150 1.9% 840.18112 2 76670 97520 11320 0.0% 0113 1 69850 22220 6830 9.8% 6845.3114 3 89370 133680 21310 3.3% 2949.21115 0 78220 60650 4290 15.0% 11733116 3 58940 126350 10620 7.2% 4243.68117 3 90460 101000 11190 8.4% 7598.64118 1 66970 49830 4050 11.3% 7567.61119 3 73780 36360 16420 7.6% 5607.28120 1 88910 52420 5680 7.2% 6401.52121 2 73100 90030 7220 9.4% 6871.4122 2 35000 13540 9900 10.9% 3815123 3 46840 49490 16110 0.0% 0124 2 102960 98590 9970 4.8% 4942.08125 3 38320 109310 3250 7.2% 2759.04126 4 25150 55610 11900 6.6% 1659.9127 1 52460 37820 2450 7.5% 3934.5128 1 65850 76890 13180 7.0% 4609.5129 2 33140 97840 11330 0.3% 99.42130 2 114810 106680 11470 10.7% 12284.67

131 2 48300 56650 8650 5.2% 2511.6132 2 46960 15440 5000 3.5% 1643.6133 4 60240 59510 10780 12.5% 7530134 1 87580 95190 1740 12.3% 10772.34135 3 77080 89110 13180 1.1% 847.88136 2 69020 98460 9290 5.4% 3727.08137 2 103880 86070 3870 15.0% 15582138 1 53310 51480 7350 8.5% 4531.35139 2 91270 118430 3790 10.8% 9857.16140 2 36970 38720 4860 3.9% 1441.83141 2 25610 36930 7240 6.6% 1690.26

142 1 70860 96660 12970 2.7% 1913.22143 1 73050 89210 2910 9.1% 6647.55144 1 82600 125180 9840 2.8% 2312.8




145 2 45580 63090 7350 7.3% 3327.34146 2 31360 39560 1910 3.4% 1066.24147 1 111880 97300 15070 14.8% 16558.24148 1 77890 93980 5640 7.8% 6075.42149 2 50350 53710 10680 2.3% 1158.05

150 2 55330 78080 200 13.7% 7580.21151 4 36410 69470 13140 3.2% 1165.12152 2 79870 85440 8030 7.8% 6229.86153 0 106560 77630 8480 14.4% 15344.64154 2 109180 106570 14830 3.0% 3275.4155 3 85930 47860 6520 7.9% 6788.47156 3 82060 68330 6150 10.3% 8452.18157 3 77040 71310 11480 0.0% 0158 1 93640 94130 10230 8.2% 7678.48159 1 76040 51790 7510 7.6% 5779.04160 2 52530 103960 10500 8.2% 4307.46161 2 59950 78980 13670 3.9% 2338.05162 3 66380 99630 11060 7.2% 4779.36163 3 103620 145260 18860 1.9% 1968.78164 3 53110 94680 11730 7.1% 3770.81165 4 89610 185460 19870 0.0% 0166 2 86120 92170 2060 15.0% 12918167 2 47740 68390 4980 3.6% 1718.64168 3 49240 78220 12680 0.0% 0169 3 59270 76940 12140 10.9% 6460.43170 1 79050 72910 14400 8.3% 6561.15171 0 79740 54710 3090 10.3% 8213.22172 3 16650 53530 16210 0.0% 0173 1 59250 13590 0 15.0% 8887.5174 2 58140 46000 7190 10.1% 5872.14175 1 91970 88710 6590 4.9% 4506.53176 3 73150 116170 14820 0.0% 0177 2 84990 66780 11320 11.0% 9348.9178 3 79900 106840 15720 4.3% 3435.7179 2 101760 74260 15230 10.2% 10379.52180 1 53500 74580 12190 3.0% 1605181 1 75330 78800 10330 12.0% 9039.6182 3 32010 55310 6470 3.5% 1120.35183 3 78230 77720 15570 3.4% 2659.82

184 3 50700 89490 7580 6.3% 3194.1185 3 10770 35160 12590 0.0% 0186 3 64670 116990 11860 0.8% 517.36187 2 31640 63620 11890 10.5% 3322.2188 2 83170 87790 6810 14.8% 12309.16189 2 104640 62030 3720 15.0% 15696190 2 79910 108590 10420 7.7% 6153.07191 1 71870 71570 8040 9.0% 6468.3192 1 82800 92230 14590 8.1% 6706.8193 2 37310 5070 7720 10.3% 3842.93194 2 125830 116960 15510 10.4% 13086.32




4.2 PROBLEM FORMULATION

Firstly we identify the independent variables as :

x1= Number of dependent children

x2= Combined annual salary of husband and wifex3= Current mortgagex4= Other debts

Now we define dependent variable as

Y= Investment amount

Investment as a percentage of salary is given in Retirementplan.xls. We have calculated investmentamount for all 194 couples using the following :

Investment Amount(Y) = Invested % x Combined annual salary

4.3 SCATTER PLOT ANALYSIS

We often study the relationship between variables using graphical methods. A simple graph thatcan be used to study the relationship between two variables is called a scatter plot.

1) Investment Amount V/S Dependent Childeren

This scatter plot indicates that there is no significant correlation between invested amount and

number of dependent children. So we cannot conclude that with a change in independent variable

(Number of Childeren) , the dependent variable (Investment amount) will also change.

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

I n v e s t e

d a m o u n t

No Of children

Invested amount V/S no of children scatterplot




2) Investment Amount V/S Combined Salary

This scatterplot indicates there is indeed a positive correlation between the independent variable (

Salary) and the dependent variable (Investment amount). Points tend to rise from bottom left to top

right but relationship is not perfect.

Interpretation : In most of the cases dependent variable ( Investment amount) will increase with

increase in independent variable (Salary).

3) Investment Amount V/S Mortgage on Home

0

5000

10000

15000

20000

25000

0 20000 40000 60000 80000 100000 120000 140000

I n v e s t m e n t a m o u n t

Salary amount

Invested amount vs salary scatter plot

0

5000

10000

15000

20000

25000

0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

I n v e s t e

d A m o u n t

Mortgage amount

Invested amount vs Mortgage scatter plot




This scatterplot indicates there is very little positive correlation between the independent variable

(Mortgage on home) and the dependent variable (Investment amount). The relationship is not

perfect.


increase in independent variable (mortgage).

4) Investment Amount V/S Other Debts

This scatterplot indicates there is very little positive correlation between the independent variable

(Debts) and the dependent variable (Investment amount). The relationship is not perfect.


increase in independent variable (Debts).

4.4 CORRELATION ANALYSIS:

Correlations are numerical summary measures that indicate the strength of relationships between

pairs of variables. A correlation between a pair of variables is a single number that summarizes the

information in a scatterplot.

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000

I n v e s t e

d A m o u n t

Debt amout

Invested amount vs debt scatter plot




Covariance :

A covariance is a single number that measures the strength of the linear relationship between two

variables. By looking at the sign of the covariance or correlation — plus or minus — we can tell

whether the two variables are positively or negatively related.

It can be calculated by using the following formula :

We calculated using Excel function:

=Covar(array1, array2)

Correlation coeffcients (r)Between no of children and invested amount -0.40077Between salary and invested amount 0.685392Between mortgage amount and invested amount 0.010924Between debt amount and invested amount -0.26176

Variance:

The variance is a parameter describing in part either the actual probability distribution of an

observed population of numbers, or the theoretical probability distribution of a not-fully-observed

population of numbers.

It is calculated by using the following formula :

We calculated using Excel function :

=Variance(P)

Variance (Var)Inveted amount (Y) 19247458No of dependent children per family (X1) 0.901823Salary drawn (X2) 5.48E+08Mortgage amount (X3) 9.04E+08Other Debt amount (X4) 23884527

http://en.wikipedia.org/wiki/Population_parameter

http://en.wikipedia.org/wiki/Population_parameter




Correlation Coefficient:

It is a measure of the strength of the linear relationship between two variables that is defined in

terms of the (sample) covariance of the variables divided by their (sample) standard deviations.

It is calculated by using the following formula :

We calculated it using the following Excel function :

=CORREL( X -range, Y -range)

Correlation coeffcients (r)Between no of children and invested amount -0.40077Between salary and invested amount 0.685392Between mortgage amount and invested amount 0.010924Between debt amount and invested amount -0.26176

Interpretation :

We can see there exists high positive correlation between Salary and the invested amountwhich was evident from the scatter plot as well.

A slight positive correlation exists between Mortgage amount and the invested amount as

the coefficient of correlation is 0.010.

As the coefficient of correlation between Debt and Invested amount is negative there exists

a negative correlation between them.

4.5 REGRESSION ANALYSIS

The Regression Model :

Dependent variable Investment Amount (y) is function of all four independent variables Number of

dependent children (x1), Combine salary of husband and wife (x2), mortgage on home (x3) and

other debt (x4).

Y = f(x1, x2, x3, x4)




So we can write dependent variable Investment Amount (y) in terms of all four independent

variables Number of dependent children (x1), Combine salary of husband and wife (x2), mortgage

on home (x3) and other debt (x4) as following

Y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε

Where

β0, β1, β2, β3 and β4 – Regression parameters relating the mean value of independent variable y to

x1, x2, x3 and x4.

ε - Is an error that describes the effects on y of all factors other than the values of independent

variables x1, x2, x3 and x4.

Now we minimise the effect of error term ε while forming regression equation using Ordinary

Least Square Method (OLS) we get following regression equation:

Yˆ = β0ˆ + β1ˆx1 + β2ˆx2 + β3ˆx3 + β4ˆx4

Now we do regression analysis using data analysis tool of Microsoft Excel and get following

Regression StatisticsMultiple R 0.80005212R Square 0.64008339Adjusted R Square 0.6324661Standard Error 2666.59834Observations 194ANOVA

Df SS MS F SignificanceF

Regression 4 2390075800 597518950 84.03040864 7.07731E-41Residual 189 1343931124 7110746.689

Total 193 3734006924




Regression Analysis:-

Multiple Coefficient of Determination (R^2):-

In case of multiple regression we consider adjusted R^2 instead of normal R^2 to determine howmuch variation in dependent variable is explained by independent variable in regression equation.

In given output adjusted R^2 = 0.6324 so we can say that about 63% variation in dependentvariable is explained by independent variables in regression equation.

Test for significance of regression model:-

Now we test overall validity of regression model by hypothesis testing method using ANOVAtable.

We define null and alternate hypothesis as

H 0 : All independent variables are insignificant

H 1 : At least one independent variable is significant.

That is

H 0 : All the B i are zero.

H 1 : At least one B i is non-zero.

From ANOVA table we get that

Significant F value (P value) : 7.07731E-41

Now we define confident level (1- α) % to be 95% so level of significance ( α) is 0.05.

Here F value (P value) < level of significance ( α)

Hence we reject null hypothesis H 0. We conclude that at least one independent variable amongstx1, x2, x3 and x4 is significant in regression model to define dependent variable InvestmentAmount. Hence overall regression model is significant.

Test for significance independent variables of regression model:-

Now we test significance of independent variables of regression model by hypothesis testing

method.We define null and alternate hypothesis as

H 0 : Particular independent variables is insignificant

H 1 : Particular independent variable is significant.

Testing for Number of Dependent Children (x1) :

H 0 : B1 = 0. H 1 : B1 ≠ 0

From table we get thatP value: 0.88213




And level of significance ( α) = 0.05.

Here P value > level of significance ( α)

Hence we accept hypothesis H 0. We conclude that independent variable number of dependentchildren x1 is not significant in regression model to define dependent variable Investment Amount.

Testing for Combine Salary of Husband and Wife (x2) :

H 0 : B2 = 0. H 1 : B2 ≠ 0 From table we get that

P value: 0. 2.51E-34


Here P value < level of significance ( α)

Hence we reject hypothesis H 0. We conclude that independent variable Salary of Husband and Wife(x2) is significant in regression model to define dependent variable Investment Amount.

Testing for Combine Mortgage on Home (x3) :


P value: 4.38E-06



Hence we reject hypothesis H 0. We conclude that independent variable Combine Mortgage onHome (x3) is significant in regression model to define dependent variable Investment Amount.

Testing for other debt (x4) :


P value: 3.08E-06



Hence we reject hypothesis H 0. We conclude that independent variable other debt (x4) is significantin regression model to define dependent variable Investment Amount.

Since number of dependent children x1 is insignificant independent variable, we redefineregression equation as

Yˆ = β0ˆ + β2ˆx2 + β3ˆx3 + β4ˆx4




Regression :

Dependent variable Investment Amount (y) is function of all four independent variables Combinesalary of husband and wife (x2), mortgage on home (x3) and other debt (x4).

Y = f(x2, x3, x4)

So we can write dependent variable Investment Amount (y) in terms of all four independentvariables Number of dependent children (x1), Combine salary of husband and wife (x2), mortgageon home (x3) and other debt (x4) as following

Y = β0 + β2x2 + β3x3 + β4x4 + ε

Where

β0, β2, β3 and β4 – Regression parameters relating the mean value of independent variable y to x2,x3 and x4.

ε - Is an error that describes the effects on y of all factors other than the values of independentvariables x2, x3 and x4.

Now we minimise the effect of error term ε while forming regression equation using Ordi naryLeast Square Method (OLS) we get following regression equation:

Yˆ = β0ˆ + β2ˆx2 + β3ˆx3 + β4ˆx4

Now we do regression analysis using data analysis tool of Microsoft Excel and get following

Regression Statistics

Multiple R 0.800026R Square 0.640041Adjusted RSquare 0.634358Standard Error 2659.727Observations 194ANOVA

df SS MS F Significance F Regression 3 2.39E+09 7.97E+08 112.6128 6.18568E-42Residual 190 1.34E+09 7074147

Total 193 3.73E+09Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept -350.683392 700.9336248 -0.50031 0.617437 -1733.29472 1031.927937Salary 0.158133126 0.009258688 17.07943 3.07E-40 0.139870103 0.176396148Mortgage -0.04011113 0.007930723 -5.05769 9.96E-07 -0.055754703 -0.02446755Debt -0.22192098 0.043524152 -5.0988 8.23E-07 -0.3077736 -0.13606836




RESIDUAL OUTPUT

Observation

Predicted Invested amount Residuals

1 9931.572242 -4176.3722422 7832.329254 2052.8207463 10723.47578 -3348.8757794 4639.17154 1271.908465 8492.257697 3122.2423036 646.7911716 -646.79117167 7287.003743 -2979.9637438 3091.920204 -1400.3502049 965.8980698 -965.8980698

10 1172.64797 5074.55203

11 10505.46692 -725.926919612 4967.238102 -3228.07810213 2607.99913 1592.8608714 8177.048746 -1782.96874615 -231.3033727 2640.30337316 8586.373364 8056.12663617 5084.870983 298.969016518 6992.249539 -3080.93953919 3249.05506 3322.4449420 6876.126283 -1890.36628321 11147.06493 4313.43507522 5489.310945 -2107.19094523 6783.843479 2020.32652124 7046.09042 2920.2095825 11537.61844 1510.82156126 6228.207497 5941.99250327 5577.62728 -2235.6672828 3704.682636 -3704.68263629 9019.316476 -3695.46647630 -496.1986071 2281.79860731 9070.99109 -1671.63109

32 1230.382747 -1230.38274733 7160.026184 1612.53381634 -35.04830719 35.0483071935 3550.971882 727.788117836 1827.335017 4812.02498337 6864.641727 -3235.20172738 7562.623129 -502.30312939 9643.330661 2524.58933940 9595.571767 -2286.46176741 1485.118915 -1485.118915

42 8482.676941 397.883059343 5336.169539 -826.419538544 7455.729637 -698.9796372




45 5593.387183 -367.18718346 9246.898958 -1787.35895847 5288.495461 2018.15453948 4547.630653 -4547.63065349 4363.381291 -3402.98129150 4897.780882 -1596.02088251 2011.412855 -19.2928548152 6045.582181 3067.99781953 9153.266002 1103.13399854 2668.445078 170.724922455 613.4047715 -613.404771556 5385.514867 2178.08513357 977.7586403 -281.608640358 3650.319917 -1496.55991759 9942.198698 -149.9186979

60 1146.920022 -602.870021961 11390.85538 -4198.95537762 2686.58377 -1086.3037763 5190.176508 -532.046508264 3058.775806 2518.79419465 6877.920656 -2980.83065666 8051.262476 -4140.39247667 12615.88292 -1874.76292368 4572.165196 1393.51480469 9776.231422 4562.268578

70 11858.23542 2984.26458371 -3127.336278 3127.33627872 4543.849693 1519.20030773 1439.696854 -1076.27685474 3553.83348 1046.4265275 2671.117123 -2671.11712376 8219.707949 2009.29205177 14214.82413 5594.17587278 4247.50272 -2212.8627279 7187.554245 -2844.75424580 1415.796535 -1415.79653581 6682.0859 -5812.185982 632.9276517 973.392348383 6317.08562 3232.6643884 7834.794862 -581.754862285 3113.685806 -2032.60580686 3919.010507 -3919.01050787 1252.027159 500.972840988 8805.45685 -790.796850489 4275.328903 -331.888902790 4774.45973 -1858.81973

91 2000.869343 316.57065792 14731.31868 3922.68131793 5608.234045 -3998.174045




94 9768.787478 1562.24252295 2231.135495 -593.49549596 12273.93684 4894.22316497 7455.360062 1430.63993898 9021.843009 224.536991499 6859.137281 -646.3772813

100 2663.733965 1298.686035101 4044.493108 -1882.593108102 5753.021655 -1821.521655103 2933.530428 -374.4904276104 6629.074602 5726.425398105 5330.882606 2467.017394106 1777.657368 -1777.657368107 8811.313549 3695.686451108 8522.421846 -3563.451846

109 6319.23432 -1490.01432110 5367.691494 540.8085058111 344.3398309 495.8401691112 5349.600469 -5349.600469113 8287.925816 -1442.625816114 3690.482096 -741.2720959115 8633.708672 3099.291328116 1544.84098 2698.83902117 7419.519268 179.1207316118 7341.974465 225.6355346

119 6213.995394 -606.7153944120 10345.79621 -3944.276212121 5995.373604 876.0263963122 2443.853572 1371.146428123 1496.025367 -1496.025367124 9763.59476 -4821.51476125 603.1872261 2155.852774126 -1245.074898 2904.974898127 5884.271052 -1949.771052128 4053.31962 556.1803796129 -1548.989259 1648.409259130 10980.09179 1304.578214131 3095.234583 -583.6345825132 5346.327429 -3702.727429133 4395.934576 3134.065424134 9294.294826 1478.045174135 5338.996619 -4491.116619136 4552.677194 -825.5971938137 11764.98658 3817.013423138 4383.35336 147.9966402139 8490.685394 1366.474606

140 2863.859349 -1422.029349141 611.0940223 1079.165978142 4099.172957 -2185.952957




143 6976.837514 -329.2875137144 5506.29912 -3193.49912145 2695.294086 632.0459137146 2597.706068 -1531.466068147 10094.08858 6464.15142148 6945.027468 -869.6074684149 3086.834613 -1928.784613150 5222.561265 2357.648735151 -295.6181772 1460.738177152 7070.288951 -840.4289511153 11504.26555 3840.374449154 9348.560007 -6073.160007155 9871.052621 -3082.582621156 8520.11337 -67.93337013157 6423.91507 -6423.91507

158 8410.990211 -732.5102114159 7929.777497 -2150.737497160 1455.926351 2851.533649161 2927.760637 -589.7106369162 3695.475579 1083.884421163 6023.098667 -4054.318667164 1646.912034 2123.897966165 1971.045981 -1971.045981166 9113.541358 3804.458642167 3350.225383 -1631.585383

168 1484.341094 -1484.341094169 3241.595921 3218.834079170 6029.575573 531.574427171 9378.636312 -1165.416312172 -3462.254756 3462.254756173 8473.594051 413.9059494174 5402.452703 469.687297175 9172.102594 -4665.572594176 3268.17586 -3268.17586177 7898.284192 1450.615808178 4510.08241 -1074.38241179 9382.434414 997.0855861180 2412.734002 -807.7340023181 6108.284198 2931.315802182 1056.782625 63.56737521183 5447.324326 -2787.504326184 2394.960046 799.1399538185 -2851.882126 2851.882126186 2551.201941 -2033.841941187 -537.8618494 3860.061849188 7768.610712 4540.549288

189 12882.72745 2813.272548190 5617.650479 535.4195214191 6359.346102 108.9538983




192 5805.462787 901.3372134193 3632.670103 210.259897194 11413.81564 1672.504355

Regression Analysis:-

Multiple Coefficients of Determination (R^2):-

In case of multiple regression we consider adjusted R^2 instead of normal R^2 to determine howmuch variation in dependent variable is explained by independent variable in regression equation.

In given output adjusted R^2 = 0.6343 so we can say that about 63.5% variation in dependentvariable is explained by independent variables in regression equation.

Test for significance of regression model:-

Now we test overall validity of regression model by hypothesis testing method using ANOVAtable.


H 0 : All independent variables are insignificant

H 1 : At least one independent variable is significant.

That is

H 0 : All the B i are zero.

H 1 : At least one B i is non-zero.

From ANOVA table we get that

Significant F value (P value) : 6.18568E-42

Now we define confident level (1- α) % to be 95% so level of significance ( α) is 0.05.

Here F value (P value) < level of significance ( α)

Hence we reject null hypothesis H 0. We conclude that at least one independent variable amongstx2, x3 and x4 is significant in regression model to define dependent variable Investment Amount.Hence overall regression model is significant.

Test for significance independent variables of regression model:-

Now we test significance of independent variables of regression model by hypothesis testingmethod.


H 0 : Particular independent variables is insignificant

H 1 : Particular independent variable is significant.




Testing for Combined Salary of Husband and Wife (x2) :


P value: 3.07E-40



Hence we reject hypothesis H 0. We conclude that independent variable Salary of Husband and Wife(x2) is significant in regression model to define dependent variable Investment Amount.

Testing for Combine Mortgage on Home (x3) :


P value: 9.96E-07



Hence we reject hypothesis H 0. We conclude that independent variable Combine Mortgage onHome (x3) is significant in regression model to define dependent variable Investment Amount.

Testing for other debt (x4) :


P value: 8.23E-07



Hence we reject hypothesis H 0. We conclude that independent variable other debt (x4) is significantin regression model to define dependent variable Investment Amount.

All the independent variables and overall regression model is significant. So we find regressionequation by substituting regression parameters from excel out as following:

Yˆ = -350.683 + 0.158 x2 - 0.040 x3 - 0.221 x4

Interpretation from equation:-

1. With one dollar change in combine salary of husband and wife, investment amount willchange by 0.158 dollars considering all other independent variables kept constant.

2. With one dollar change in mortgage on home, investment amount will change by 0.040dollars considering all other independent variables kept constant.




3. With one dollar change in other debt, investment amount will change by 0.221 dollarsconsidering all other independent variables kept constant.

4. Intercept -350.686 takes care in defining total investment amount of all other parametersother than mentioned independent variables.

4.6 RESDUAL PLOTS AND NORMAL PROBABILITY CURVE:

The following residual plots are obtained by the regression analysis in excel for all the threeindependent variables with respect to the dependent variable.

Fanning effect present therefore Heteroskedasticity is present No rainbow pattern present therefore no Non-linearity No linear increasing/ Decreasing trend observed therefore No Auto-Correlation

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Mortgage Residual Plot




No Fanning effect present therefore Heteroskedasticity is not present No rainbow pattern present therefore no Non-linearity No linear increasing/ Decreasing trend observed therefore No Auto-Correlation

No Fanning effect present therefore Heteroskedasticity is not present No rainbow pattern present therefore no Non-linearity No linear increasing/ Decreasing trend observed therefore No Auto-Correlation

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Debt Residual Plot

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Salary Residual Plot




Now we will be doing the verification of the assumptions of the regression analysis.

The assumptions are :

1) The Regression model should be Linear.

To check the linearity, we refer to the residual plot for all the three independent variables. Now asthere is no rainbow pattern in any of the residual plot curves, then we can conclude that the modelis linear.

2) The error variance should be constant that is no heteroskedasticity should be present.

To check the heteroskedasticity we again refer to the residual plots for all the three independentvariables.In the residual plot of the mortgage value we observe a Fanning effect. But no fanning effect ispresent in the Debt residual plot and the salary residual plots. So we conclude thathetereskedasticity is present among the independent and the dependent variables.

3) Error variances should be independent that is no Auto-Correlation should be present.

To check the Autocorrelation we again refer to the residual plots for all the three independentvariables. For the residual plots of all the independent variables no linearly increasing / decreasingtrend is observed. So we can conclude that there is no Auto Correlation present among any of theindependent variables and the dependent variable

4) The error should follow normal distribution.

To check this assumption we observe the Normal Probability plot. As the Normal probability plotshows almost a linear relationship we can conclude that the error follows a normal distribution.

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Normal Probability Plot




SECTION – 5 CONCLUSION

So after verifying all the assumptions we can conclude that although there is a bit of

heteroskedasticity present in this regression model but still we can accept the model to forecast the

investment amount in the retirement plan for each of the families , depending on the given

variables.



SECTION – 6 MANAGERIAL IMPLICATION

Documents

Bs Project Grp 8