To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in millions of dollars) for 23 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) 1363.9 150 1218.4 72 678.2 63 583.8 35 455.5 33 412.5 31 314.4 24 285.1 18 252.9 18 165.5 17 146.6 16 145.6 16 142.5 16 122.1 16 118.9 15 111.5 15 102.1 15 94.2 13 87.3 9 72.2 7 54.1 5 40.3 2 4.5 2 The least squares regression equation is y=enter your response here+enter your response herex. (Round to three decimal places as needed.) Determine the estimate of the standard deviation. s=enter your response here (Round to two decimal places as needed.) What is the test statistic for the hypotheses? t=enter your response here (Round to two decimal places as needed.) What is the p-value for the test statistic? p-value=enter your response here (Round to three decimal places as needed.) State the conclusion at α=0.05. Since the p-value is less less greater than α, there is sufficient insufficient sufficient evidence to reject H0. Conclude there is a a no linear relationship between revenue and message rate. What is the value for the coefficient of determination r2? r2=enter your response here (Round to two decimal places as needed.) Interpret the value of r2 in the context of this problem. A. r2 is the proportion of the sample points that do not fit within the 95% confidence interval. B. r2 is the proportion of the total sample variability around message rate that is explained by the linear relationship between the revenue and the message rate. C. r2 is the proportion of the sample points that fit on the estimated linear regression line. D. r2 is the proportion of the total sample variability around mean revenue that is explained by the linear relationship between the revenue and the message rate. Create a 95% confidence interval for the slope β1. Select the correct choice below and fill in the answer box(es) if necessary. (Round to three decimal places as needed.) A. β1≥enter your response here B. enter your response here≤β1≤enter your response here C. β1≤enter your response her

To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in millions of dollars) for 23 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) 1363.9 150 1218.4 72 678.2 63 583.8 35 455.5 33 412.5 31 314.4 24 285.1 18 252.9 18 165.5 17 146.6 16 145.6 16 142.5 16 122.1 16 118.9 15 111.5 15 102.1 15 94.2 13 87.3 9 72.2 7 54.1 5 40.3 2 4.5 2 The least squares regression equation is y=enter your response here+enter your response herex. (Round to three decimal places as needed.) Determine the estimate of the standard deviation. s=enter your response here (Round to two decimal places as needed.) What is the test statistic for the hypotheses? t=enter your response here (Round to two decimal places as needed.) What is the p-value for the test statistic? p-value=enter your response here (Round to three decimal places as needed.) State the conclusion at α=0.05. Since the p-value is less less greater than α, there is sufficient insufficient sufficient evidence to reject H0. Conclude there is a a no linear relationship between revenue and message rate. What is the value for the coefficient of determination r2? r2=enter your response here (Round to two decimal places as needed.) Interpret the value of r2 in the context of this problem. A. r2 is the proportion of the sample points that do not fit within the 95% confidence interval. B. r2 is the proportion of the total sample variability around message rate that is explained by the linear relationship between the revenue and the message rate. C. r2 is the proportion of the sample points that fit on the estimated linear regression line. D. r2 is the proportion of the total sample variability around mean revenue that is explained by the linear relationship between the revenue and the message rate. Create a 95% confidence interval for the slope β1. Select the correct choice below and fill in the answer box(es) if necessary. (Round to three decimal places as needed.) A. β1≥enter your response here B. enter your response here≤β1≤enter your response here C. β1≤enter your response her

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

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Related questions

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

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)
1363.9 150
1218.4 72
678.2 63
583.8 35
455.5 33
412.5 31
314.4 24
285.1 18
252.9 18
165.5 17
146.6 16
145.6 16
142.5 16
122.1 16
118.9 15
111.5 15
102.1 15
94.2 13
87.3 9
72.2 7
54.1 5
40.3 2
4.5 2

The least squares regression equation is

y=enter your response here+enter your response herex.

(Round to three decimal places as needed.)

Determine the estimate of the standard deviation.

s=enter your response here

(Round to two decimal places as needed.)

What is the test statistic for the hypotheses?

t=enter your response here

(Round to two decimal places as needed.)

What is the p-value for the test statistic?

p-value=enter your response here

(Round to three decimal places as needed.)

State the conclusion at

α=0.05.

Since the p-value is

less

greater

than

α,

there is

sufficient

insufficient

sufficient

evidence to reject

H0.

Conclude there is

linear relationship between revenue and message rate.

What is the value for the coefficient of determination

r2?

r2=enter your response here

(Round to two decimal places as needed.)

Interpret the value of

in the context of this problem.

is the proportion of the sample points that do not fit within the 95% confidence interval.

is the proportion of the total sample variability around message rate that is explained by the linear relationship between the revenue and the message rate.

is the proportion of the sample points that fit on the estimated linear regression line.

is the proportion of the total sample variability around mean revenue that is explained by the linear relationship between the revenue and the message rate.

Create a 95% confidence interval for the slope

β1.

Select the correct choice below and fill in the answer box(es) if necessary.

(Round to three decimal places as needed.)

β1≥enter your response here

enter your response here≤β1≤enter your response here

β1≤enter your response here

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