Question

An instructor asked a random sample of eight students to record their study times at the beginning of a course. She then made a table for total hours studied (x) over 2 weeks and test score (y) at the end of the 2 weeks. The table is given below. Complete parts (a) through (d). X 11 1512 208 15 16 21 0 y 91 76 83 75 89 77 80 80 Ex= 118, Ey= 651, Exy = 9,464, Ex2 = 1,876 mazinco. (Exivi - (Ex) (Evi) n)2 a. Compute SST, SSR, and SSE, using the formulas, SST = Ey? - (yi)2/n, SSR= -, and SSE = SST - SSR. Ex? - (Ex)2/n SST = (Round to two decimal places as needed.) SSR = (Round to two decimal places as needed.) SSE = (Round to two decimal places as needed.) b. Compute the coefficient of determination, r2. 2 = (Round to four decimal places as needed.) c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. % (Round to two decimal places as needed.) d. State how useful the regression equation appears to be for making predictions. Choose the correct answer below. O O Moderate to high usefulness Low usefulness

Answer 1

12 Σ*y 121 11 15 12 91 76 y2 8281 5776 1001 1140 225 144 400 6889 64 5625 7921 5929 6400 996 1500 712 1155 1280 77 225 256 80 21 80 441 6400 1680 118 651 1876 53221 9464 η Σx=118, Σx2 =1876, Σy=651, Σy? =53221, ΣΧy=9464 S -Σχο. Σε =1876 - 19 -135.5 Sss Σy Σν 53221 - 651) -245.875 Sax ΣΧΥ - ΣΕΣ» = 9464 - 118.651 =138.25

a) SST ==Ly2 (Cy)2 =245.875 SSD - (Exy - n )-(-138.25)2 = 141.0558 Ex2 - (592) (135.5) SSE ESST-SSR=245.875–141.0558 =104.8192 b) Coefficient of determination r2 = 1 * =1-407 = 1-0.4263 =0.5737 SST 245.875 c) There are 57.37% of variation in the observed value of the response variable is explained by the regression equation d) The variation is about 57.37% it is moderate usefulness 1st option is correct