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# Regression analysis

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The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought "new" two years ago and each sold "used" within the past month. For each Cadet in the sample, we have listed both the mileage, (in thousands of miles), that the Cadet had on its odometer at the time it was sold used, and the price, (in thousands of dollars), at which the Cadet was sold used. Also given are the products of the mileages and used selling prices for each of the fifteen Cadets.
24.2 27.3
15.2 34
29.2 26.7
28.2 25.5
34.4 25.5
23.3 32.8
20.9 31.4
27.9 30.1
23.9 28.5
25.7 26.7
23 31.2
26.9 31.1
37.7 22.3
20.9 31.6
24.1 30.7

What is the value of the sameple correlation coefficient for these data?

Bivariate data obtained for the paired variables and are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is ^y=53.31 -1.03x.

21.8 32.2
24.3 26.2
25.6 26.9
28.5 23.3
29.4 24.1

For the data point (28.5,23.3),the value of the residual is __________.

The least-squares regression line given above is said to be a line which "best fits" the sample sata. The term "best fits is used because the line has an equation that minimizes the _____________, which for these data is _________.

The total variation in the sample y values is given by the ________________, which for these data is _______.

The value r2 is the proportion of the total variation in the sample y values that is explained by the estimated lionear relationship between x and y. For theses data, the value of r2 is ____________.