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-23733-0.81 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 107.7 155.1 117.3 135.2 127.8 139.8 138.3 116.6 151.1 120.0 25.0700 280.6630 473.4976 50.6517 35.8561 75.8118 64.5291 280.2276.20 25.6137338.5968 177.9556 140 80.5865 3.4596 0.2228 41.73 16130 110 213.0035 764.5982 976.8720 sums 10 120 130 140 150160 Send data Jto Excel Figure 1 Answer the following:

Answer 1

1)total variation is given by SSy =$\sum$(y-$\overline{y}$)² which for this data is 976.8720

2) the value of r² is =764.5982/ 976.8720=0.78

3)

residual =actual-predicted= 135.2-(237.33-117.3*0.81)=-7.12

4)

that minimizes the sum of square of error SSE =$\sum$(y-$\widehat{y}$)^{2   which for this data is 213.0035}