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   Stories, y
768   52
628   48
518   45
511   43
491   38
478   35

(a) x=501 ft

(b) x=641 ft

(c) x=318 ft

(d) x=730 ft

Find the regression equation.

ModifyingAbove y with caretyequals=____xplus+left parenthesis ____ right parenthesis

​(Round the slope to three decimal places as needed. Round the​ y-intercept to two decimal places as​ needed.)

Choose the correct graph to show this

(a) Predict the value of y for

xequals=five hundred and one

Choose the correct answer below.

A. 51

B. 47

C. 40

D. not meaningful

​(b) Predict the value of y for

xequals=641

Choose the correct answer below.

A. 47

B. 31

C. 40

D. not meaningful

​(c) Predict the value of y for

xequals=318

Choose the correct answer below.

A. 31

B. 47

C. 51

D. not meaningful

(d) Predict the value of y for

xequals=730

Choose the correct answer below.

A. 40

B. 31

C. 51

D. not meaningful

Answer 1

Find X⋅Y and X2 as it was done in the table below.

X	Y	X⋅Y	X⋅X
768	52	39936	589824
628	48	30144	394384
518	45	23310	268324
511	43	21973	261121
491	38	18658	241081
478	35	16730	228484

Slope = 0.049

Intercept = 15.71

( a ) if x=501 then

y = 15.71 + 0.049 ( 501 )

= 40.259

= 40

( b ) if x=641 then

y = 15.71 + 0.049 ( 641 )

= 47.119

= 47

( c ) if x=318 then

y = 15.71 + 0.049 (318 )

= 31.292

= 31

( d ) if x=730

y = 15.71 + 0.049 (730 )

= 51.48

= 51