Question

92 98 Test score, y Student Study Hours, 67 3 85 5 87 5 7 10 a. Computer to two decimal places and give a qualitative meaning to r. b. Compute the coefficient of determination, r, to two decimal places and state the meaning of r in the context of the problem. c. Write the equation of the Line of Best Fit for the given data. Compute the slope and the y-intercept to two decimal places.

Answer 1

Solution:

a.

Х Y X*Y X2 Y2 67 3 201 4489 9 85 5 425 7225 25 87 5 435 7569 25 92 7 644 8464 49 98 10 980 9604 100 Sum = 429 30 2685 37351 208 The correlation coefficient r is computed using the following expression: = SSXY SSxx SSyy where 72 SSxy=xY n i=1 2 (Ex) (9) $$x = x -+( S$= - () ΣΧ; i=1 2 1 i=1 In this case, based on the data provided, we get that 1 SSxy = 2685 - (429 x 30) = 111 SSxx = 37351 (429)= 542.8 SSyy = 208 – (30)2 = 28 Therefore, based on this information, the sample correlation coefficient is computed as follows TE SSXY SSxx SSyy 111 542.8 x 28 - 0.9

b.

Then, the coefficient of determination, or R-Squared coefficient (R), is computed by simply squaring the correlation coefficient that was found above. So we get: R? 0.90042 0.8107

c.

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows: m = SSXY 111 - 0.2045 SSxx 542.8 n=Y - X.m= 6 - 85.8 x 0.2045 = -11.5457 Therefore, we find that the regression equation is: Y = -11.5457 +0.2045X

Scatter Plot and Regression Line 9.60 7.60 Y 5.60 3.60 1.68.80 65.80 70.80 75.80 80.80 85.80 90.80 95.80 100.80 Regression equation: Y = -11.5457 + 0.2045 * X