6--3. Regression methods were used to analyze the data from
a study investigating the relationship between roadway surface
temperature (x) and pavement deflection (y). The data follow.
Temperature
1
Temperature
X
Deflection
y
X
Deflection
y
70.0
0.621
72.7
0.637
77.0
0.657
67.8
0.627
72.1
0.640
76.6
0.652
72.8
0.623
73.4
0.630
78.3
0.661
70.5
0.627
74.5
0.641
72.1
0.631
74.0
0.637
71.2
0.641
72.4
0.630
73.0
0.631
75.2
0.644
72.7
0.634
76.0
0.639
71.4
0.638
EXERCISES FOR SECTION 6--2
(a) Estimate the intercept ~0 and slope ~ 1 regression coefficients. Write the estimated regression line.
(b) Compute the residuals.
(c) Compute SSE and estimate the variance.
(d) Find the standard error of the slope and intercept coefficients.
(e) Show that SSr =SSR + SSE·
(f) Compute the coefficient of determination, R2 . Comment
on the value.
(g) Use a t-test to test for significance of the intercept and
slope coefficients at a =0.05 . Give the P-values of each
and comment on your results.
(h) Construct the ANOVA table and test for significance of
regression using the P-value. Comment on your results
and their relationship to your results in part (g).
(i) Construct 95% Cls on the intercept and slope. Comment
on the relationship of these Cls and your findings in parts
(g) and (h).
(j) Perform model adequacy checks. Do you believe the
model provides an adequate fit?
(k) Compute the sample correlation coefficient and test for its
significance at a = 0.05. Give the P-value and comment
on your results and their relationship to your results in
parts (g) and (h).
2
EXERCISES FOR SECTION 6--2
6--9. Consider the data and simple linear regression in
Exercise 6-3.
(a) Find the mean deflection given that the temperature is
74.0 degrees.
(b) Compute a 95% CI on this mean response.
(c) Compute a 95% PI on a future observation when temperature is equal to 74.0 degrees.
(d) What do you notice about the relative size of these two
intervals? Which is wider and why?
3
EXERCISES FOR SECTION 6--2