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1. The regression model 
was fitted to a data set obtained from 20 runs of an experiment in which two predictors 
and 
were observed along with the response 
. The least squares estimates were
; 
; 
Predict the response for
a) 
; 
b) ; 
2. The following model was fitted to a sample of 25 families in order to explain household milk consumption
where
-milk consumption, in liters per week
-weekly income, in hundreds of dollars
-family size
The least squares estimates of the regression parameters were
; 
; 
a) Interpret the estimates 
and 
b) Is it possible to provide a meaningful interpretation of the estimate a?
3. The following model was fitted to a sample of 20 students using data
obtained at the end of the education year. The aim was to explain students’
weight gains.
where
-weight gained, in kilograms, during the academic year
-average number of meals eaten per week
-average number of exercise per week, (in hours)
-average number of beers consumed per week
The least squares estimates of the regression parameters were
; 
; 
; 
a) Interpret the estimates 
and 
b) Is it possible to provide a meaningful interpretation of the estimate a?
4. In the study of exercise 2, where the least squares estimates were based on 25 sets of sample observations, the following data were found
and 
a) Find and interpret the coefficient of determination.
b) Find the adjusted coefficient of determination.
5. In the study of exercise 3, sample of 20 observations were used to calculate the least squares estimate. The regression sum of squares and error sum of squares were found to be
and 
a) Find and interpret the coefficient of determination.
b) Find the adjusted coefficient of determination.
6. A multiple linear regression was fitted to a data set obtained from 27 runs of an experiment, in which four predictors 
and 
were observed along with the response y. The following results were obtained:
; 
; 
; 
;
; 
a) Predict response for 
b) Estimate the error standard deviation 
c) What proportion of the y variability I explained by the fitted regression?
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| Adjusted coefficient of determination | | | Computer solution of multiple regressions |