Example 2: Use least-squares regression to fit a straight line to x and y values given below. Along with the slope and intercept, compute the standard error of the estimate and the correlation...

Subject: NUMERICAL METHODS

Directions: In example no. 2, the problem and solution are both given. Please answer letter a.

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Extracted text: Example 2: Use least-squares regression to fit a straight line to x and y values given below. Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the regression line. 4. 11 12 15 17 19 9 8 7 y 5 7 10 12 12 nEx¡yt-Ex; £ yi η Σx2-Σ x)2 10(911)-(95)(82) %3D n = 10 Σy82 a, = = 0.3524699599 10(1277)-(95)z Ex¡yi = 911 95 = 9.5 10 ao = ỹ – ajã = 8.2 – 0.3524699599(9.5) = 4.851535381 Σχ 1277 = = 8.2 ΣΧ 95 Therefore, the least square fit is: y = 4.851535381 + 0.3524699599x Least-Squares Fit of a Straight Line 14 Standard error of the estimate 12 Sr Vn-2 Evi-ao-a;x;)² %3D п-2 10 9.073965287 8 Sy = = 1.0650097 10-2 6 Correlation coefficient 4 EGi-y)²-E(y;-ao-a,x;)? r2 = St-Sr - St 55.60-9.073965287 r2 = 55.60 10 15 20 r2 = 0.8367991855 r = 0.9147672849 a.) Repeat the problem Example 2, but regress x versus y - that is, switch the variables. Interpret your results. Plot the data and the regression line. Interpret your results. 4 9. 11 12 15 17 19 y 6 7 6 9 8 7 10 12 12