Find the equation of the regression line for the given data. Then construct a sc
ID: 3205876 • Letter: F
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