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

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The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 63 inches. Is the result close to the actual weight of 562 ​pounds? Use a significance level of 0.05. Chest_size_(inches)   Weight_ (pounds)58                                  41450                                  31265                                  49959                                  45059                                  45648                                  260 What is the regression equation?^y = ____ + _____ x (round to one decimal place as needed.)What Is the best predicted weight of a bear with a chest size of 63 inches? ^y =____ pounds (round one decimal as needed)Is the result close to the actual weight of 452 pounds?(a) This result is very close to the actual weight of the bear.(b) This result is close to the actual weight of the bear.(c) This result is exactly…

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion. In particular, note the variables Barefoot and Footwear2. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear2 represents their range of ankle motion (in degrees) while wearing medical shoes. Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing medical shoes, ?̂ , based on their range of ankle motion while barefoot, ? . Round your coefficients to two decimal places of precision. ?̂  = A physical therapist determines that her patient Jan has a range of ankle motion of 7.26°7.26° while barefoot. Predict Jan's range of ankle motion while wearing medical shoes, ?̂ . Round your answer to two decimal places. ?̂ = Suppose Jan's…

Identify whether this statement is True or False and provide justification for your answer. “A positive correlation between attitude and intention will always result in a significant effect between the two variables in regression analysis.”

Does the Regression line give information about all the data points in the data set? Does the Regression line usually have all the points in the data set on it?

The data shows a systolic and a diastolic blood pressure of certain patients.  Find the linear regression eqation, using the first variable  (systolic) as the independent variable.  Find the best predicted diastolic blood pressure for a patient with a systolic blood pressure reading of 140.  Use a significance level of x Systolic Diastolic 116 82 124 88 112 72 144 95 138 96 112 76 145 88 124 76 130 90 129 94 1)Find the correlation coefficient.  2)State the appropriate critical r value to use to test the claim that the correlation between systolic blood pressure and diastolic blood pressure is significantly different from 0 3)The correlation between diastolic blood pressure and systolic blood pressure is: significant, not significant, weak, none  4)The best predicted diastolic blood pressure for a patient with a systolic blood pressure reading of 140 is closest to 1pts