Question

To study how social media may influence the products consumers​ buy, researchers collected the opening weekend box office revenue​ (in millions of​ dollars) for 23recent movies and the social media message rate​(average number of messages referring to the movie per​ hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue​ (y) and message rate​ (x).

To study how social media may influence the products consumers​ buy, researchers collected the opening weekend box office revenue​ (in millions of​ dollars) for

2323

recent movies and the social media message rate​(average number of messages referring to the movie per​ hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue​ (y) and message rate​ (x).

To study how social media may influence the products consumers​ buy, researchers collected the opening weekend box office revenue​ (in millions of​ dollars) for

2323

recent movies and the social media message rate​(average number of messages referring to the movie per​ hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue​ (y) and message rate​ (x).

Message Rate		Revenue​ ($millions)
1363.2		146
1219.2		79
681.2		67
583.6		37
454.7		35
413.9		34
306.2		21
289.8		18
245.1		18
163.9		17
148.9		16
147.4		15
147.3		15
123.6		14
118.1		13
108.9		13
100.1		12
90.3		11
89.1		6
70.1		6
56.2		5
41.6		3
8.4		1

Message Rate		Revenue​ ($millions)
1363.21363.2		146146
1219.21219.2		7979
681.2681.2		6767
583.6583.6		3737
454.7454.7		3535
413.9413.9		3434
306.2306.2		2121
289.8289.8		1818
245.1245.1		1818
163.9163.9		1717
148.9148.9		1616
147.4147.4		1515
147.3147.3		1515
123.6123.6		1414
118.1118.1		1313
108.9108.9		1313
100.1100.1		1212
90.390.3		1111
89.189.1		66
70.170.1		66
56.256.2		55
41.641.6		33
8.48.4		11

The least squares regression equation is

y=−0.031+ 0.086x. ​(Round to three decimal places as​ needed.)

Check the usefulness of the hypothesized model. What are the hypotheses to​ test?

A.H0​:β1≠0 against Ha​:β1=0

B.H0​:β0=0 against Ha​:β0≠0

C.H0​:β0≠0 against Ha​:β0=0

D.H0​:β1=0 againstHa​:β1≠0 Your answer is correct.

Determine the estimate of the standard deviation.

s=9.59​(Round to two decimal places as​ needed.)

What is the test statistic for the​ hypotheses?

t=15.14 ​(Round to two decimal places as​ needed.)

What is the​ p-value for the test​ statistic?

​p-value=0 ​(Round to three decimal places as​ needed.)State the conclusion at α=0.05.

Since the​ p-value is less than α​, there is sufficient evidence to reject H0.

Conclude there is a linear relationship between revenue and message rate.What is the value for the coefficient of determination r2?

r2=_____(Round to two decimal places as​ needed.).

2 parts remaining

Answer 1

Let's use excel:

Step 1) First enter the given data set in excel columns.

Step 2) Then click on Data >>> Data Analysis >>>Regression >>>>OK

Step 3) Input Y Range: Select the data of column "B"

Input X Range: Select the data of column "A" .

Click on Labels:

then Click on Output Range

Look the following Image

1 Message Rate Revenue (Smillions) 1363.2 1219.2 681.2 583.6 454.7 413.9 306.2 289.8 245.1 163.9 148.9 147.4 147.3 123.6 118.1 108.9 100.1 90.3 89.1 70.1 56.2 146 79 67 37 35 34 21 18 18 17 16 15 15 14 13 13 12 Regression Input 4 OK Input Y Range Input X Range Labels $B$1:$B$24 $A$1:$A$24 Constant is Zero 6 Cancel Help 10 Confidence Level: 95 % Output options 12 13 14 15 16 17 18 19 20 21 SD$1 Output Range New Worksheet Ply New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability | | Normal Probability Plots 23 41.6 3

Then Click on OK, we get following result.

From the above output the p-value and R² are as follows:

p-value = 0.000

R² = 0.916