Lab Activity 12 - Multiple Linear Regression Data Set: “Temperature”The data are the geographic latitude, mean January temperature, mean April temperature, and mean August temperature (in degrees Fahrenheit) for 20 U.S. Cities. The data, (Temperature.txt), is provided in Datasets folder on ANGEL and are summarized in the table below.

City Latitue JanTemp AprTemp AugTemp

MiamiFL 26 67 75 83

HoustonTX 30 50 68 82

MobileAL 31 50 68 82

DallasTX 33 43 66 85

PhoenixAZ 33 54 70 92

LosAngelesCA 34 58 63 75

MemphisTN 35 40 63 81

NorfolkVA 37 39 57 77

SanFranciscoCA 38 49 56 64

BaltimoreMD 39 32 53 76

KansasCityMO 39 28 55 76

WashingtonDC 39 31 53 74

PittsburghPA 40 25 50 71

ClevelandOH 41 25 48 70

NewYorkNY 41 32 53 76

BostonMA 42 29 48 72

SyracuseNY 43 22 46 68

MinneapolisMN 45 12 46 71

PortlandOR 46 40 51 69

DuluthMN 47 7 39 64

1.

Use software to fit a multiple linear regression model with response Y = latitude, and predictors X1 = JanTemp, X2 = AprTemp, and X3 = AugTemp. (Note that we do not use the ‘City’ variable.) Paste the output below and provide the regression equation.

In Minitab Express: Statistics > Regression > Multiple Regression (MAC) OR Statistics > Multiple Regression (PC). Put “latitude” in the response box, and the three predictors in the “Continuous predictors” box.

2.

Interpret the slopes for each predictor by following the format of this statement:“Assuming the other predictors are held constant, for every one degree Fahrenheit increase in __________, the city’s expected latitude will (increase/decrease) by _________.”Note that you should have three sentences here – one for each of the three predictors. 3.

For each of the following hypotheses, provide the test statistic and p-value from the output and make a conclusion based on your findings. The first one has been done for you. a. H0: β1 = 0 vs. HA: β1 ≠ 0, where β1 is the coefficient for X1 = JanTemp The test statistic is t =1.629 and p-value = 0.1228. Since the p-value > .05, we accept the null hypothesis. We conclude that JanTemp is NOT significant in predicting latitude while AprTemp and AugTemp are also in the model. b. H0: β2= 0 vs. HA: β2 ≠ 0, where β2 is the coefficient for X2 = AprTemp

c. H0: β3 = 0 vs. HA: β3 ≠ 0, where β3 is the coefficient for X3 = AugTemp 4.

Create a scatterplot of Y = latitude versus X1 = JanTemp.

In Minitab Express: Graph > Scatterplot > Simple. Put “latitude” in the “Y” box and “JanTemp” in the “X” box.

a. Comment on what you see. Is there a linear relationship? If so, is it a negative or positive relationship? Would you say it is strong or weak? b. Is the coefficient for JanTemp negative or positive? c. Does what you found in parts (b) and 3(a) match what you found in the scatterplot from part(a)?

d. Think about the conclusion given in 3(a) and the fact that the scatterplot is only plotting the response versus just JanTemp. Can you provide a possible explanation for what you’ve observed in part (c)? 5.

Identify the ANOVA table in your output and answer the following questions to conduct the ANOVA F-test. a. What are the null and alternative hypotheses for the ANOVA F-test? b. What is the test statistic and p-value? c. Make a decision based on the p-value and state a conclusion.

6.

Using the output, complete this statement: “The proportion of variation in Latitude (response) that is explained by mean January temperature, mean April temperature, and mean August temperature (predictors) is _________.”

7.

First, by hand, use the regression equation to predict the latitude for a city with JanTemp = 40, AprTemp = 60, and AugTemp = 70. Then, verify your solution using software.

In Minitab Express: Statistics > Regression > Predict (MAC) OR Statistics > Predict Regression (PC). Enter the new X values in the appropriate boxes.