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1. Construct a 99% prediction interval for the Acres/Gardener ratio for a household with a Consumers/Gardener ratio equal to 2. Construct a 99% confidence interval for the mean Acres/Gardener ratio among households with a Consumers/Gardener ratio equal to 2. State the interpretation of each interval and explain why they are different. (Do this both in math(typed) and r code please)

2. Compute the fitted residuals. Do it "manually" and check your values using the `lm()` function in R. Check that the two vectors are equal using the `all.equal()` function or by computing their mean squared error (MSE) or another measure of discrepancy. Compute the residual standard error ($\hat\sigma$) and compare it with the summary output of your `lm` object. (Do this both in math(typed) and r code please)

3. Use the fitted residuals to investigate the assumptions of homoskedasticity and linearity in the model. The SLR model sometimes also assumes that the residuals are Normally distributed. Investigate this by making a QQ plot of the fitted residuals. Do you see any evidence of deviations from any of the three assumptions? Do you note any outliers? (Do this both in math(typed) and r code please)

Data set:

consumers acres 1 1 1.71 2 1.08 1.52 3 1.15 1.29 4 1.15 3.09 5 1.2 2.21 6 1.3 2.26 7 1.37 2.4 8 1.37 2.1 9 1.43 1.96 10 1.46 2.09 11 1.52 2.02 12 1.57 1.31 13 1.65 2.17 14 1.65 2.28 15 1.65 2.41 16 1.66 2.23 17 1.87 3.04 18 2.03 2.06 19 2.05 2.73 20 2.3 2.36

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