We will continue the analysis of height and wages in Britain.

(a) Estimate the model with income at age 33 as the dependent variable and height at age 33 as the independent variable. (Exclude observations with wages above 400 British pounds per hour and height less than 40 inches.) Interpret the \(t\) statistics on the coefficients.

(b) Explain the \(\mathrm{p}\) values for the two estimated coefficients.

(c) Show how to calculate the 95 percent confidence interval for the coefficient on height.

(d) Do we accept or reject the null hypothesis that \(\beta_{1}=0\) for \(\alpha=0.01\) and a two-sided alternative? Explain your answer.

(e) Do we accept or reject the null hypothesis that \(\beta_{0}=0\) (the constant) for \(\alpha=0.01\) and a two-sided alternative? Explain.

(f) Limit the sample size to the first 800 observations. Do we accept or reject the null hypothesis that \(\beta_{1}=0\) for \(\alpha=0.01\) and a twosided alternative? Explain if/how/why this answer differs from the earlier hypothesis test about \(\beta_{1}\).