Bo + B1x + u, suppose that E(u) # 0. Letting a, = E(u), In the simple linear regression model y = show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.

could someone teach me how to do the first 4?

A box office analyst seeks to predict opening weekend box office gross for movies. Toward this​ goal, the analyst plans to use online trailer views as a predictor. For each of the 66 ​movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross​ (in millions of​ dollars) are collected and stored in the accompanying table. A linear regression was performed on these​ data, and the result is the linear regression equation Yi=−0.840+1.4108Xi. Determine the coefficient of​ determination,r2​,and interpret its meaning. Determine the standard error of the estimate. How useful do you think this regression model is for predicting opening weekend box office​ gross? Can you think of other variables that might explain the variation in opening weekend box office​ gross?

A box office analyst seeks to predict opening weekend box office gross for movies. Toward this​ goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross​ (in millions of​ dollars) are collected and stored in the accompanying table. A linear regression was performed on these​ data, and the result is the linear regression equation Yi=−1.254+1.3968Xi.   Complete parts​ (a) through​ (d). a. Determine the coefficient of​ determination,r2​,and interpret its meaning. b. Determine the standard error of the estimate.   c. How useful do you think this regression model is for predicting opening weekend box office​ gross?   d. Can you think of other variables that might explain the variation in opening weekend box office​ gross?

A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below.   Time 10 8 6 13 19 18 27 10 7 Money 58 25 41 51 84 81 87 45 15 1. The equation of the linear regression line is:   ˆyy^ = ______ +_____ xx   (Please show your answers to two decimal places)

A study tests the effect of earning a Master's degree on the salaries of professionals. Suppose that the salaries of the professionals (S,) are not dependent on any other variables. Let D, be a variable which takes the value 0 if an individual has not earned a Master's degree, and a value 1 if they have earned a Master's degree. What would be the regression model that the researcher wants to test? A. S,= Po + B,D,+u, i=1, .. , n. O B. S,= Po + B, + u, i= 1, .. , n. OC. 1=6o +B1,S, + u, i= 1, .. , n. O D. 0=Bo +B, S, + u,, i= 1, .. , n. Suppose that a random sample of 160 individuals suggests that professionals without a Master's degree earn an average salary of $59,000 per annum, while those with a Master's degree earn an average salary of $80,000 per annum. The OLS estimate of the coefficient B, will be $ and that of B, will be $ Click to select your answer(s). DELL

The​ least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30​% of adults 25 years and older have at least a​ bachelor's degree.

A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…

In Step 2: Construct an estimated simple linear regression model how did you come up with the column X*X ?

A linear regression analysis reveals a strong, negative linear relationship between x and y. Which of the following could possibly be the results from this analysis? (A) ŷ 13.1 27.4x, r = 0.85 (B) == 27.4+ 13.1x, r = -0.95 (D) == (C) ŷ 13.1+ 27.4x, r = 0.95 542 385x, r = -0.15 (E) 0.85 0.25x, r = -0.85