Graph the following observations of \(x\) and \(y\) on graph paper.

a. Using a ruler, draw a line that fits through the data. Measure the slope and intercept of the line you have drawn.

b. Use formulas (2.7) and (2.8) to compute, using only a hand calculator, the least squares estimates of the slope and the intercept. Plot this line on your graph.

c. Obtain the sample means \(\bar{y}=\sum y_{i} / N\) and \(\bar{x}=\sum x_{i} / N\). Obtain the predicted value of \(y\) for \(x=\bar{x}\) and plot it on your graph. What do you observe about this predicted value?

d. Using the least squares estimates from (b), compute the least squares residuals \(\hat{e}_{i}\).

e. Find their sum, \(\sum \hat{e}_{i}\), and their sum of squared values, \(\sum \hat{e}_{i}^{2}\).

f. Calculate \(\sum x_{i} \hat{e}_{i}\).

Data From Formula 2.7 and 2.8:-

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TABLE 2.4 Exercise 2.3 Data x 1 2 3 y 6 4 11 49 69 17 53 13