Assignment _2- Fergie Mc Nish

QUANTITATIVE FOUNDATIONS Assignment II

Name of Student: Fergie Mc Nish Student ID: 806005929 Date Submitted: August 31, 2014

FERGIE MC NISH: 806005929

INTF6001: QUANTITATIVE FOUNDATIONS Page 1

QUESTION #8 Table 1: Model Summary - Overall Model Fit

The Model Summary gives us a measure of how well our overall model fits and how well our predictors; location, advertisement, age and income is able to predict sales of RY stocks

Multiple Correlation Coefficient [R] Multiple correlation coefficient [R] is a measure of the strength of the relationship between the sales of RY stocks and the predictors; location, advertisement, age and income. In this case R= 0.982 which tells us theres a strong direct relationship.

Coefficient of Determination [R Square- R2] The coefficient of determination [R Square- R2] statistic enables us to determine the amount of explained variation [variance] in sales of RY stocks from the four [4] predictors; location, advertisement, age and income. R Square varies between zero [0] and one [1].

Conclusion The R Square indicates that 96.5% of the variations in the dependant variable [sales of RY stocks] are explained by changes in the independent variable [location, advertisement, age and income]. The regression equation appears to be very useful for making predictions since the value of R2 is close to 1. The overall fit is very good. The unexplained variables account for 3.5% [100% - 96.5%].



Table 2: Coefficients - Parameter Estimates

Table 2- Coefficients is used to identify which predictors are significant contributors to the 96.5% of explained variance in sales of RY stocks [i.e., R2 = 0.965] and which ones are not.

Dependent variable - Sales of RY stocks Independent variables - Location, Advertisement, Age and Income

Hypothesis H0: = 0 [This independent variable is not a significant predictor of the dependent variable.] H1: 0 [This independent variable is a significant predictor of the dependent variable.]

Decision Rule If p-value [sig. value] < 0.05 reject the Null Hypothesis [H0] If p-value [sig. value] > 0.05 fail to reject the Null Hypothesis [H0]

Conclusion The coefficient for advertisement [0.537] is not a significant predictor in sales of RY

stocks because its p-value is 0.211, which is larger than 0.05. The coefficient for income [0.065] is not a significant predictor in sales of RY stocks

because its p-value is 0.052, which is larger than 0.05. The coefficient for age [0.095] is not a significant predictor in sales of RY stocks

because its p-value is 0.215 which is larger than 0.05. The coefficient for location [0.983] is not a significant predictor in sales of RY stocks

because its p-value is 0.104 is larger than .05. The intercept [constant] is not a significant predictor in sales of RY stocks because its

p-value is 0.138, which is larger than 0.05. The constant and the four [4] independent variables; advertisement, income, age and location do not have any significant impact on the sales of RY stocks.



Table 3: ANOVA Analysis of Variance

Since R Square is not a test of statistical significance [it only measures explained variation in sales of RY stocks from the predictor; location, advertisement, age and income], the F-ratio is used to test whether or not R Square [R2] could have occurred by chance alone. In short, the F-ratio found in the ANOVA table measures the probability of chance departure from a straight line

Dependent variable - Sales of RY stocks Independent variables - Location, Advertisement, Age and Income

Hypothesis H0: All the independent variables equal to zero [0]]. None of the independent variables are

significant predictors of the dependent variable, sales of RY stocks] H1: At least one independent variable is different from zero [0]. At least one of the independent

variables is a significant predictor of the dependent variable, sales of RY stocks]

Decision Rule If p-value [sig. value] < 0.05 reject the Null Hypothesis [H0] If p-value [sig. value] > 0.05 fail to reject the Null Hypothesis [H0]

Conclusion Since the sig. value [0,000] for the ANOVA table is less than 0.05; therefore at least one of the independent variables [location, advertisement, age and income] is statistically significant. In other words, at least one of these variables has an impact on the sales of RY stocks.



QUESTION #9 Categorical financial data is captured by the table given. There are both nominal data and ordinal data.

The name of the test conducted is the Chi-square test for independence, also called Pearsons Chi-square test or the Chi-square test of association. This test is used to discover if there is a relationship between two categorical variables.

Null Hypothesis: H0 Alternative Hypothesis: H1

Hypothesis H0: Type of Financial Institutions and Level of Strict Financial Regulations are independent; no

relationship exists between Type of Financial Institutions and Level of Strict Financial Regulations.

H1: Type of Financial Institutions and Level of Strict Financial Regulations are dependent; a relationship exists between Type of Financial Institutions and Level of Strict Financial Regulations.

Decision rule If p-value [sig. value] < 0.05 reject the Null Hypothesis [H0] A relationship exists between Type of Financial Institutions and

Level of Strict Financial Regulations. If p-value [sig. value] > 0.05 fail to reject the Null Hypothesis [H0] No relationship exists between Type of Financial Institutions and

Level of Strict Financial Regulations.

Conclusion The p-valve [sig. value] of 0.007 is less that 0.05 which means that the researcher should reject the null hypothesis [H0]; a relationship exists between of Financial Institutions and Level of Strict Financial Regulations.



QUESTION #10 The T-Test is a statistical examination of two population mean. A two-sample T-Test examines whether two samples are different and is commonly used when the variances of two normal distributions are unknown and when an experiment used a small sample size.

Null Hypothesis: H0 Alternative Hypothesis: H1

Hypothesis H0: Blackberry stock price = Nokia stock price

[The population means of Blackberry stock price and Nokia stock price are the same] H0: 1 = 2 or H0: 1 - 2 = 0

H1: Blackberry stock price Nokia stock price [The population means of Blackberry stock price and Nokia stock price are different] H1: 1 2 or

H1: 1 - 2

0

Decision rule If p-value [sig. value] < 0.05 reject the Null Hypothesis [H0] There is no difference in mean Blackberry stock price and the

Nokia stock price. If p-value [sig. value] > 0.05 fail to reject the Null Hypothesis [H0] There is a difference in mean Blackberry stock price and the Nokia

stock price.

Conclusion The p-valve [sig. value] of 0.0000 is less that 0.05 which means that the researcher should reject the null hypothesis [H0]; therefore the population means of Blackberry stock price and Nokia stock price are different.



QUESTION #11 Combinations: nCr The order is not important once the items are in the box. n = what we have r = what we want

a)

= 8C27C4

= [28] [35]

= 980

Conclusion Two [2] low risk stocks and four [4] high risk stocks can be selected by an investor in 980 ways.

Sector Level of Risk Number of shares available [n]

Number of shares we want [r]

Energy Low 8 2 Housing High 7 4



b)

= 8C37C3

= [56] [35]

= 1,960

Conclusion Three [3] low risk stocks and three [3] high risk stocks can be selected by an investor in 1,960 ways.

c) If the investor chooses the first combinations of two [2] low risk stocks and four [4] high risk stocks the investor will have 980 choices. On the other hand if the investor chooses the second combinations of three [3] low risk stocks and three [3] high risk stocks the investor will have 1,960 choices. Therefore is the investors wants the combinations with the most number of choices, the investor should select the second combination of three [3] low risk stocks and three [3] high risk stocks. The second combination will give the investor 980 [1,960=980] more choices than the first combinations.

Sector Level of Risk Number of shares available [n]

Number of shares we want [r]

Energy Low 8 3 Housing High 7 3

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Assignment _2- Fergie Mc Nish