Find the equation of the regression line for the given data. Then construct a sc

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 766 620 520 508 494 484

Stories, y 51 46 52 24 38 34

(a) x= 501 feet (b) x= 651 feet (c) x=310 feet (d) x=731 feet

Find the regression equation. ModifyingAbove y with caret =____x+(____) (Round the slope to three decimal places as needed.

Round the y-intercept to two decimal places as needed.)y for xequals 501 . Choose the correct answer below.

A. 37

B. 51

C. 46

D. not meaningful

(b) Predict the value of y for x= 651 . Choose the correct answer below.

A. 46

B. 37

C. 26

D. not meaningful

(c) Predict the value of y for x= 310 . Choose the correct answer below.

A. 26

B. 46

C. 51

D. not meaningful (d) Predict the value of y for x= 731 . Choose the correct answer below.

A. 37

B. 26

C. 51

D. not meaningful

Explanation / Answer

a. Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=3392 , Y=245 , XY=142046 , X2=1977912

Step 3: Use the following equations to find a and b:

ab=YX2XXY/nX2(X)2=24519779123392142046/61977912339227.652

b=nXYXY/nX2(X)2=61420463392245/61977912(3392)20.059

Step 4: Substitute a and b in regression equation formula

. y = a + bx= 7.652 + 0.059x

a. Now for x=501 y=37.2=37A is answer

b. For x=651, y=46.06=46 so A is answer

c. For x=310, y=25.94=26 so A is answer

d. For x=731, y=50.78=51 so c is answer

X Y XY XX 766 51 39066 586756 620 46 28520 384400 520 52 27040 270400 508 24 12192 258064 494 38 18772 244036 484 34 16456 234256

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