Linear Regression Questions

1. You are studying the relationship between weight and height. You draw a random
sample of 200 individuals and collect each individual W=weight (in pounds) and
H=height (in inches), and estimate the following model:
W = β0+β1* H+ε
You estimate the coefficients β0=–91.4 (t-statistic=44.02) and β1=4.02 (tstatistic=8.51). The R^2 for the regression is 0.77.
a) Plot graphically the relationship between weight and height.
b) What is the predicted weight for an individual who is 65 inches tall?
c) If someone grows 2 inches over the course of a year, what is the predicted
increase in her weight?
d) Can you give an interpretation for the coefficient β0? Does it make sense?
e) Explain in plain words the explanatory power of this model.
2. You are estimating the following regression model:
Y = β0+β1* X+ε
For each hypothesis and each available data, conclude whether you (i) reject the
hypothesis, (ii) fail to reject the hypothesis, or (iii) do not have enough information to
conclude anything. Please explain your reasoning.
a) You are testing the null that the coefficient β1 equals zero (with a two-tailed
alternative hypothesis); you learn that the t-statistic for the coefficient β1 is 2.91.
Use a significance level α=0.05.
b) You are testing the null that the coefficient β1 equals zero (with a two-tailed
alternative hypothesis); you learn that the estimated coefficient is 8.44. Use
α=0.05.
c) You are testing the null that the coefficient β1 equals zero (with a two-tailed
alternative hypothesis); you learn that the p-value for the coefficient β1 is 0.08.
Use α=0.05.
d) You are testing the null that the coefficient β1 equals zero (with the alternative
hypothesis being the coefficient is bigger than zero); you learn that the t-statistic
for the coefficient β1 is –1.78. Use α=0.05.
e) You are testing the null that the coefficient β1 equals zero (with a two-tailed
alternative hypothesis); you learn that the estimated coefficient is 5.82 and the
standard error of the estimate is 2.80. Use α=0.05.