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 comma xHeight, x	768	628	518	511	491	478		​(a) x = 503 feet	​(b) x = 641 feet
​Stories, y	52	48	50	27	38	34		​(c) x = 798 feet	​(d) x = 726 feet

Find the regression equation.

ModifyingAbove y with caretyequals=nothingxplus+left parenthesis nothing 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 below.

A. 0800060Height (feet)Stories

A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (748, 32), (608, 38), (498, 40), (491, 17), (471, 28), (458, 24). A trend line that falls from left to right passes through the points (200, 41), and (600, 37). All coordinates are approximate.

B. 0800060Height (feet)Stories

A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (768, 52), (628, 48), (518, 50), (511, 27), (491, 38), (478, 34). A trend line that rises from left to right passes through the points (200, 19), and (600, 44). All coordinates are approximate.

C. 0800060Height (feet)Stories

A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (778, 57), (638, 53), (528, 55), (521, 32), (501, 43), (488, 39). A trend line that rises from left to right passes through the points (200, 29), and (600, 54). All coordinates are approximate.

D. 0800060Height (feet)Stories

A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (758, 34), (608, 33), (488, 35), (461, 27), (331, 28), (278, 34). A trend line that falls from left to right passes through the points (200, 35), and (600, 30). All coordinates are approximate.​(a) Predict the value of y for

x = 503.

Choose the correct answer below.

A. 52

B. 46

C. 38

D. not meaningful

​(b) Predict the value of y for

x = 641.

Choose the correct answer below.

A. 56

B. 46

C. 38

D. not meaningful

​(c) Predict the value of y for

x = 798.

Choose the correct answer below.

A. 56

B. 52

C. 46

D. not meaningful

​(d) Predict the value of y for

x = 726.

Choose the correct answer below.

A. 38

B. 52

C. 56

D. not meaningful

Answer 1

a) Scatter Plot :

Answer: Option B. 0800060Height (feet)Stories

A scatterplot has a horizontal axis labeled Height in feet from 0 to 800 in increments of 200 and a vertical axis labeled Stories from 0 to 60 in increments of 10. The following points are plotted: (768, 52), (628, 48), (518, 50), (511, 27), (491, 38), (478, 34). A trend line that rises from left to right passes through the points (200, 19), and (600, 44). All coordinates are approximate.

b) The least square regression line is

The least square regression equation is

​(a) Predict the value of y for x = 503.

(b) Predict the value of y for x = 641.

c) Predict the value of y for x = 798.

​(d) Predict the value of y for x = 726