Practice Multiple Regression

Page 1 of 25

Practice Multiple Regression

By | November 2012
Page 1 of 25
Multiple Regression in SPSS
I.

STAT 314

The accompanying data is on y = profit margin of savings and loan companies in a given year, x1 = net revenues in that year, and x2 = number of savings and loan branches offices. x1
3.92
3.61
3.32
3.07
3.06
3.11
3.21
3.26
3.42

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.

x2
7298
6855
6636
6506
6450
6402
6368
6340
6349

y
0.75
0.71
0.66
0.61
0.70
0.72
0.77
0.74
0.90

x1
3.42
3.45
3.58
3.66
3.78
3.82
3.97
4.07

x2
6352
6361
6369
6546
6672
6890
7115
7327

y
0.82
0.75
0.77
0.78
0.84
0.79
0.70
0.68

x1
4.25
4.41
4.49
4.70
4.58
4.69
4.71
4.78

x2
7546
7931
8097
8468
8717
8991
9179
9318

y
0.72
0.55
0.63
0.56
0.41
0.51
0.47
0.32

Determine the multiple regression equation for the data.
Compute and interpret the coefficient of multiple determination, R2. At the 5% significance level, determine if the model is useful for predicting the response. Create scatterplots to check Assumption 1 as well as to identify potential outliers and potential influential observations.

Obtain the residuals and studentized residuals, and create residual plots. Decide whether or not it is reasonable to consider that the assumptions for multiple regression analysis are met by the variables in questions.

At the 5% significance level, does it appear that any of the predictor variables can be removed from the full model as unnecessary?
Obtain and interpret 95% confidence intervals for the slopes, βi, of the population regression line that relates net revenues and number of branches to profit margin. Are there any multicollinearity problems (i.e., are net revenues and number of branches collinear [estimating similar relationships/quantities])?

Obtain a point estimate for the mean profit margin with 3.5 net revenues and 6500 branches. Test the alternative hypothesis that the mean profit margin with 3.5 net revenues and 6500 branches is greater...