Question

0 Find the equation of the regression line for the given data. The construct a scatter plot of the date and draw the regression in (The pair of we have a significant corelation) Then use the regression equation to predict the value ofy for each of the given x-vous meaningful. The table below shows the heights on tool and the number of stories of si notable buildings in a city Helght, 775 510 500 (0) 500 fot b)x500 Stories 37 (c) 318 foot x 720 Find the regression equation (Round the slope to three decimal places as needed. Round they cept to two deca places need Choose the correct graph below ОА OB Ос. OD 0 NO H (a) Predict the value of y for 500. Choose the correct answer below OA. 52 OB40 C. 47 OD not meaning th) Predict the value ofy for x640. Choose the correct answer below Click to select your answers

Answer 1

X x? Y 53 Y? 2809 775 600625 X*Y 41075 29093 619 47 383161 2209 519 44 1936 22836 508 43 269361 258064 241081 21844 37 18167 491 474 1849 1369 1296 11468 36 17064 224676 1976968 Total= 3386 260 150079

We use the above table to find the equation of regression line, which is given by:

(Y - Ybar) = b_YX ( X - Xbar ) ; where Xbar = mean of X

Ybar = mean of Y

b_XY = Cov(X,Y) / Var(X)

Now, Cou(x,y) = h Exy - 77 (150079) - (2389)(260) 325,013.166 - (564.33)(43.33) 24,452.4189 = 25,013.166 560.7477 And Var (x) = 6x + {x² - (7) ² (1976968) - ( 333c)? - -318,468.3489 - 329,494.6666 110 26 31 77 Cov(x,y) 560. 74 77 bux 11026. 3177 byx = 0.0508 Thus, the equation of regression line is: (y-7)= bx (x-²) Y-43.33 0.0508 (x 564.33) 28.6619 => Y-43.33=0.0508 X 4 = 0.0508x + 14.6621

The scatter plot of the data is given as follows:

60 50 40 Stories (Y) 30 20 Linear (Y) 10 0 o 200 400 600 800 1000 Height (X)

Answer (a):

we need to predict the value of Y for X = 500

So, put X=500 in the equation of the regression line.

Y = 0.0508*(500) + 14.6621 = 25.4 + 14.6621 = 40.0621 = 40(approx)

So, the correct option is B.

Answer (b):

Put X = 640 in the regression equation.

Y = 0.0508*(640) + 14.6621 = 32.512 + 14.6621 = 47.1741 = 47 (approx)

So, the correct option is A.

Answer (c):

Put X = 318 in the regression equation.

Y = 0.0508*(318) + 14.6621 = 16.002 + 14.6621 = 30.6641 = 31 (approx)

So, the correct option is A.

Answer (d):

Put X = 726 in the regression equation.

Y = 0.0508 *(726) + 14.6621 = 36.8808 + 14.6621 = 51.5429 = 52 (approx)

So, the correct option is B.