Q1.
a) The T-value is 3.5 and the P-value is 0.001. The chance of an association between Expend and Number of this magnitude occurring just by chance is around 1 in 1000. So we very strongly suspect that there really is an underlying association.
b) The average or expected monthly expenditure on extras this year is $12.26 for customers who did not take any options last year. For every option the customer took last year you can add another $2.79 to this.
c) The prediction equation is not very accurate. The model error measures the typical difference between the fitted values and the observed values. This is a rough estimator of the prediction error. The sample size was n=83 so there is a typical prediction error of
[pic]
which is the large in comparison with the typical size of expenditures in this data set (roughly $10-$30 judging by the given mean and standard deviation). The percentage of variation in expenditure explained by optional purchases last year is only 12%.
d) We predict $12.26+5x$2.79=$26.21
e) This is a simple regression (single input variable) and chapter 15 gave an explicit formula for the slope estimate. The equation for slope is
[pic]
and we know this equals 2.787. We also know that the standard deviation of expenditure is 14.064 and of number is 1.828. Solving for the correlation gives the answer 0.362. For simple regression, you can calculate the slope from the correlation or visa-versa. For multiple regression, it is the partial correlations that are directly related to the slopes. The formulas for this are not provided.

Q2.
a) Age is a slightly stronger predictor. The correlation is higher (0.126>0.113), the T-value is higher (1.79>1.60), the P-value is lower (0.0740.0110). Slopes are unit dependent. If I change age to months then the age slope would be 12 times smaller. Neither age nor months are good predictors however. The