Find the equation of the regression line for the given data

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\",\"Stories, y\"
772,51
628,48
518,52
508,26
496,38
483,32

(A)Find the regression equation?

(a) Predict the value of y for x=499.

Choose the correct answer below.

A.46

B.50

C.37

D.not meaningful

(b) Predict the value of y for x=648

Choose the correct answer below.

A.46

B.55

C.37

D. not meaningful

(c) Predict the value of y for x=810

Choose the correct answer below.

A.46

B.50

C.55

D.not meaningful

(d) Predict the value of y for x=724

Choose the correct answer below.

A.37

B.55

C.50

D.not meaningful

Solution

a)

Using technology, we get              
              
slope =    0.059499243          
intercept =    7.400846365          
              
Thus, the regression line is              
              
y^ =    0.059499243x   + 7.400846365

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b)

Plugging in x = 499 in the equation above:

Thus, if x =    499
  
Then  
  
y^ =    37.0909685 = 37 [answer]

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c)

Thus, if x =    648
  
Then  
  
y^ =    45.95635571 = 46 [answer]

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d)

As 810 is not within the range of values here, it is

D. NOT MEANINGFUL.

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e)

Thus, if x =    724
  
Then  
  
y^ =    50.47829817 = 50 [answer]