Question

Bivariate data obtained for the paired variables x and y 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 = -0.17+ 1.17x. In the "Calculations" table are calculations involving the observed y values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 69 -) (»-)? (3-0)? 0.6 7 2.7 2.8 4.3 4.8 4.1861 2.1345 0.0303 2.4996 4.6916 .1824 0.3364 0.2304 2.9584 2.8 5.0 5.3 0.4020 0.7762 0.0936 0.0193 0.0213 4.0804 Column sums 13.5420 1.3124 14.7880 Send data to Excel Figure 1 aoooo Shun O REGRESSION AND CORRELATION Explained and unexplained variation and the least-squares regre... 1. Fort point (1.2, 0.6), the value of the residual is I. (Round your answer to at least 2 mal places.) 2. The variation in the sample y values that is not explained by the estimated linear relationship between x and y is given by the ? , which for these data is ? 3. The value r is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value of r is I. (Round your answer to at least 2 decimal places.) 4. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the , which for these data is ? 1 x S ?

Answer 1

1)for the point (1.2,0.6 ) value of the residual =actual-predicted value =0.6-(-0.17+1.17*1.2)= -0.634

2) ..is given by sum of square of errors =$\sum$(y-$\widehat{y}$)² which for these data is 1.3124

3) r² =13.5420/14.7880 =0.916

4) ...minimizes the error(residual) sum of squares which for these data is 1.3124