(a)The multiple linear regression model is y = 0 + 1x1 + 2x2 + 3x3 + . What are the assumptions of this model?

(b) Find the 95% confidence interval for 1. 7

(c) Statistically interpret the confidence interval in (b).

(d) If you use backward elimination for variable selection, which variable will be the first one to be removed from the model? Why do you think so?

(e) Do you think there is a multicollinearity problem in this model? Why?

(f) Test for significance of regression. Write down H0 and Ha of this test, do the test, and draw a conclusion.

5. Thirty (30) samples of cheddar cheese were analyzed for their content of acetic acid, hydrogen sulfide and lactic acid. Each sample was tasted and scored by a panel of judges and the average taste score produced. The data set is shown below. ID Taste (y) Acetic (21) H2S (12) Lactic (13) 1 12.3 4.543 3.135 0.86 2 20.9 5.159 5.043 1.53 30 5.5 6.176 4.787 1.25 We fit a multiple linear regression model where "taste" is the response and all other variables are regressors. The output is given below. Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 4994.47558 1664.82519 16.22 <.0001 error corrected total root mse r-square dependent mean adj r-5q coeff var parameter estimates standard variance variable estimate t value pr> t Type 1 55 Type li SS Inflation Intercept -28.87677 19.73542 -1.46 0.1554 18057 219.72726 Acetic 0.32774 4.45976 0.07 0.9420 2314 14151 0.55427 1.83159 H25 3.91184 1-24843 3.13 0.0042 2147 01680 1007.65809 1.99220 Lactic 19.67054 8.62905 2.28 0.03 11 533.31727 533.31727 1.93791