Here are some additional review questions on ch3/13; you may also find the odd-numbered problems in the textbook helpful.
1. An experiment measured the mass of a certain variety of caterpillars after 3 weeks, in different temperatures. The results are shown below:
 Temp (C) Mass (g) 15 18 21 21 23 28 1.8 2.2 3.2 2.8 3.7 3.1
1. What is the average temperature and average mass in the study sample?

xbar = 21, ybar = 2.8

2. Calculate SS(x), SS(y), and SS(xy).

SS(x) = 98, SS(y) = 2.42, SS(xy) = 11.7

3. Find the sample correlation r.

r = SS(xy)/sqrt(SS(x) SS(y)) ≅ 0.75974 ≅ 0.76

4. Construct a 95% confidence interval on the correlation.

n = 6: about -0.05 < ρ < 0.96.

5. At a level of significance of α = 0.05, is caterpillar mass correlated with temperature?

df = n-2 = 4: 0.05 < p < 0.10: fail to reject H0; insufficient evidence to show caterpillar mass is correlated with temperature.

6. Find the equation of the best-fit line.

b1 = SS(xy)/SS(x) ≅ 0.1194, b0 = 0.2929.
Best-fit line is y = 0.2929 + 0.1194 x.

7. What does the linear model predict should be the mass of caterpillars grown at a temperature of 25 C?

y = 0.2929 + 0.1194 * 25 ≅ 3.2776 grams.

8. Find SSE, the sum of squared errors (residuals).

SSE = 1.0232.

9. What are the assumptions of the linear model?

Assumes that the sample is a random sample representative of the population. Assumes that the mass of caterpillars is normally distributed with a mean that depends upon the temperature according to the best-fit line and a standard deviation that does not depend on temperature.

10. What does the linear model predict is the standard deviation of mass of caterpillars grown at a temperature of 25 C?

se = sqrt(SSE/(n-2)) ≅ 0.5058.

11. Find SEb1, the standard error of estimate of the slope (b1) of the best-fit line.

SEb1 = se / sqrt(SS(x)) ≅ 0.0511

12. At a level of significance of α = 0.02, is the slope of the best-fit line positive?

t = (b1 - 0) / SEb1 ≅ 2.34.
df = n-2 = 4, one-tailed: 0.025 < p < 0.05
fail to reject H0: insufficient evidence to show that the slope of the best-fit regression line for mass and temperature is positive.