Explain how to use cross validation to estimate the prediction mean squared error, and the sampling distribution of the regression slope, for the problem in Exercise 7.1. If the appropriate computing...

Explain how to use cross validation to estimate the prediction mean squared error, and the sampling distribution of the regression slope, for the problem in Exercise 7.1. If the appropriate computing resources are available, implement your algorithm.

Exercise 7.1

a. Derive a simple linear regression equation using the data in Table A.3, relating June temperature (as the predictand) to June pressure (as the predictor).

b. Explain the physical meanings of the two parameters.

c. Formally test whether the fitted slope is significantly different from zero.

d. Compute the R2 statistic.

e. Estimate the probability that a predicted value corresponding to x₀
= 1013 mb will be within 1⁰C of the regression line, using Equation 6.22.

f. Repeat (e), assuming the prediction variance equals the MSE.