15. Two variables gave the follov ing data: X 20, Y= 15, O = 4, o, = 3, %3D r=+0.7 Obtain the two regression equations and find the most likely value of Y when X= 24.
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- Data is collected on the distance of several hikes (in miles), along with the amount of time (in minutes) the hike is expected to take. All hikes in the data set are between 0.5 miles and 10 miles long, and the relationship between distance and time is linear and strong. The regression equation to predict time based on distance is as follows: Predicted time = –266 + 31.48 (distance). Suppose we want to use the regression equation to predict the time it takes to complete a particular hike. For which one of the following distances would using the regression equation result in extrapolation? 1 mile 4.5 miles 6.8 miles 9 miles None of the above distances would result in extrapolation.The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 83.3 + 2.24x, + 1.30x2. The computer solution, based on a sample of eight weeks, provided SST 25.2 and SSR = 23.455. %D (a) Compute and interpret R² and R,. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R = 0.653 and R, = 0.595. Do you prefer the multiple regression results? Explain. %3D 2 Multiple regression analysi v ---Select--- ipreferred since both R2 and R, show ---Select--- O…Use the given data to find the best predicted value. If the prediction is unreliable, state so. 5) Eight pairs of data yield r = 0.742 and the regression equation y = 55.8 + 2.79x. Also, y = 71.125. What is the best predicted value of y for x = 8? Round to one decimal place.
- The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ŷ = 82.1 + 2.23x, + 1.70x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.345. (a) Compute and interpret R2 and R_2. (Round your answers to three decimal places.) . Adjusting for the number of independent variables in the model, the The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation isA popular board game manufacturer was interested in the relationship between the amount of time it takes to play a game and how well that game is rated among board game players. Information was collected on several board games and was used to obtain the regression equation ŷ = 27.273x + 18.182 where x represents the time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). What is the predicted rating of a game that takes 1 hour to play? –0.63 points 9.091 points 45.455 points 1,654.562 points
- A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00A 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). DELLYou decide to add a second independent variable to your regression. Male is a dummy variable that equals 1 if the individual is male and 0 otherwise. Your regression results are now: wage = 3.071 + 0.289 × Years of Schooling + 1.28 × Male (0.143) (0.0168) (0.624) Interpret the coefficients from this regression. Make sure to clearly indicate what is changing and what is constant in each interpretation. Determine whether each coefficient is statistically significant at each of the conventional significance levels. The R2 for this regression is 0.316. Interpret the meaning of this value.
- The estimated regression equation for a model involving two independent variables and 10 observations follows. y = 33.0798 + 0.6071x1 + 0.7058x2 a. Interpret b₁ and b2 in this estimated regression equation (to 4 decimals). b₁ = - Select your answer - b₂ = - Select your answer - b. Estimate y when *₁ = 180 and ₂ = 310 (to 3 decimals).In a fisheries researchers experiment the correlation between the number of eggs in tge nest and the number of viable (surviving ) eggs for a sample of nests is r=0.67 the equation of the regression line for number of viable eggs y versus number of eggs in the nest x is y =0.72x + 17.07 for a nest with 140 eggs what is the predicted number of viable eggs ?Two variables gave the follo ing data: Y = 15, X = 20. 4, O, = 3, r = + 0.7 %3D %3D Obtain the two regression equations and find the most likely value of Y when X= 24.