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 number of hours 6 students spent for a test and their scores on that test are shown below.

Hours spent studying, x	1	2	2	4	5	6		​(a) x=3 hours	​(b) x=4.5 hours
Test​ score, y	40	44	52	47	62	72		​(c) x=13 hours	​(d) x=3.5 hours

Find the regression equation.

y=nothingx+

​(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.

08080Hours studyingTest score

A scatterplot has a horizontal axis labeled Hours Studying from 0 to 8 in increments of 1 and a vertical axis labeled Test score from 0 to 80 in increments of 10. The following points are plotted: (2, 43), (3, 49), (3, 59), (5, 52), (6, 67), (7, 77). A trend line that rises from left to right passes through the points (2, 52), and (6, 73). All coordinates are approximate.

B.

08080Hours studyingTest score

A scatterplot has a horizontal axis labeled Hours Studying from 0 to 8 in increments of 1 and a vertical axis labeled Test score from 0 to 80 in increments of 10. The following points are plotted: (5, 39), (4, 43), (3, 51), (3, 47), (3, 59), (2, 62). A trend line that falls from left to right passes through the points (2, 54), and (6, 32). All coordinates are approximate.

C.

08080Hours studyingTest score

A scatterplot has a horizontal axis labeled Hours Studying from 0 to 8 in increments of 1 and a vertical axis labeled Test score from 0 to 80 in increments of 10. The following points are plotted: (1, 40), (2, 44), (2, 52), (4, 47), (5, 62), (6, 72). A trend line that rises from left to right passes through the points (2, 46), and (6, 67). All coordinates are approximate.

D.

08080Hours studyingTest score

A scatterplot has a horizontal axis labeled Hours Studying from 0 to 8 in increments of 1 and a vertical axis labeled Test score from 0 to 80 in increments of 10. The following points are plotted: (4, 38), (4, 43), (0, 51), (2, 46), (3, 61), (4, 71). A trend line that falls from left to right passes through the points (2, 39), and (6, 17). All coordinates are approximate.​(a) Predict the value of y for

x=3.

Choose the correct answer below.

A.

51.0

B.

53.7

C.

59.2

D.

not meaningful

​(b) Predict the value of y for

x=4.5.

Choose the correct answer below.

A.

53.7

B.

59.2

C.

105.5

D.

not meaningful

​(c) Predict the value of y for

x=13.

Choose the correct answer below.

A.

59.2

B.

105.5

C.

51.0

D.

not meaningful

​(d) Predict the value of y for

x=3.5.

Choose the correct answer below.

A.

51.0

B.

105.5

C.

53.7

D.

not meaningful

Click to select your answer(s).

Answer 1