Consider the simple linear regression model y=10+30x+e where the random error te
ID: 2908138 • Letter: C
Question
Consider the simple linear regression model y=10+30x+e where the random error term is normally and independently distributed with mean zero and standard deviation 1. Do NOT use software. Generate a sample of eight observations, one each at the levels x= 10, 12, 14, 16, 18, 20, 22, and 24.
Do NOT use software!
(a) Fit the linear regression model by least squares and find the estimates of the slope and intercept.
(b) Find the estimate of ?^2 .
(c) Find the value of R^2.
(d) Do NOT use software. Generate a new sample of eight observations,
one each at the levels of x= 10, 14, 18, 22, 26, 30, 34, and 38. Fit the model using least squares.
(e) Find R2 for the new model in part (d). Compare this to the value obtained in part (c). What impact has the increase in the spread of the predictor variable x had on the value?
Explanation / Answer
a)
b) The estimate is 4.54*4.54=20.63
c)R square is 0.07686.
SUMMARY OUTPUT Regression Statistics Multiple R 0.277236 R Square 0.07686 Adjusted R Square -0.077 Standard Error 4.54204 Observations 8 ANOVA df SS MS F Significance F Regression 1 10.30591 10.30591 0.499556 0.506203 Residual 6 123.7808 20.63013 Total 7 134.0867 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 12.77821 6.169887 2.071061 0.083764 -2.31895 27.87538 x 0.247679 0.350426 0.706793 0.506203 -0.60978 1.10514