Question

519 Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful The table below shows the heights (in feet) and the number of stories of six notable buildings in a city Height, 778 621 510 494 473 (a) x = 500 feet (b)x= 650 feet Stories, y 51 47 44 41 38 36 (c) x = 802 feet (d) x = 728 feet Find the regression equation. 9 = 0.045 x + (17.622) (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) Choose the correct graph below. OC OD A О В. 60- 60- 60 60 Q Click to select your answer(s).

Answer 1

sr.no.	height (X)	stories (Y)	X^2	Y^2	XY
1	778	51	605284	2601	39678
2	621	47	385641	2209	29187
3	519	44	269361	1936	22836
4	510	41	260100	1681	20910
5	494	38	244036	1444	18772
6	473	36	223729	1296	17028
total	3395	257	1988151	11167	148411

Date solution We have, Ex = 3395, y = 257, EX?z 198815). Ey² = 11167 EXY = 14840 Regression equation is, y = atbx. b = Sxy Sxa (EX) (ET) Say = EXT- (3399) (257) 19847 2991.833 Sax = 2 (3395) 198815T - 6 67146.83 b = Sat 5xx 17 0.045

Now, a = 7-bi EJ 257 42.83 7 = EX 3395 6 565.83 a = I by 42.83-0.64s(ses.83) a 17.62 Regression equation is, § - 17.62 0.095 X. predict value of y for x = 500 - 9 e 17,62 +0.045 X sro 39.90

b) predict value for x = 650 9 - 17.62 +0.695 X 650 46.58 ŷ 47. c) predict y value for x=802 : 9 - 17.62 +0.045 X 802 ŷ 53.36 ŷ 54 d) predict y value for x = 728. Î 17.62 to.ogs(a) À 17.62 +0.015X 728 is So. 06 50 scatter plot 0 is correct.

scatter plot stories 600 800 1000 height