Question

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, x 768 628 518 511 491 478 (a) x = 498 feet (b) x = 649 feet Stories, y 52 48 46 41 38 36 (c) x = 345 feet (d) x = 735 feet Find the regression equation (Round the slope to three decimal places as needed Round the y-intercept to two decimal places as needed.) Choose the correct graph below. ОА. ОВ. OD 60- Q 60- 60 60- Q Stories Stories Stories Stories 0 800 Height (feet) 0- 0 800 Height (feet) E 800 Height (feet) 800 Height (feet) (a) Predict the value of y for x = 498. Choose the correct answer below. Click to select your answer(s). 2

Answer 1

Let, the regression equation bei y= atba where, b - b = byr = in Ixy- (1x) (14) MIX - (1x)? and â ý - br. Now, the We from data, calculate, ă= 555.67 , Ix=3394, [x'= 42558 1983218 as = 43.5, [y= 261, [ys = 11545 150725 3 xy = 609 n=6 2 150725 (6x46005) - ( 3394 X 261) (6x 1894658) - ( 339 4 )? 0.04871708518 = 0106125803441 ba 1983218 ~ 064 0.049 A b = 0.049 15.78217 0.049 ( 506 x 565,67)= 9.60413 ^ a = o 15,78 43.5- a = 9.60 0.049. 15.78 The regressio sion equation is, V2 The option appropriate graph is: B 40.182 cas For X2 498, st ~ 40. (A) (b) For x = 649, y a 47.581 ~ 48.() (C) For #= 345, est 32.685 ^ 33 (C) (d) for N2 735 } = 51. 795 ^ 52 (A)

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