Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective r² and adjusted r2. Linear Quadratic Cubic Intercept 9.52 9.86 9.91 2.62 2.71 1.80 NA -0.31 -0.33 NA NA 0.26 0.800 0.824 0.883 Adjusted R2 0.797 0.821 0.882 a. Predict y for x =2 and 5 with each of the estimated models. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
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- Mita, the manufacturer of copiers, has been spending increasing amounts of money on radio and television advertising in recent years. An analyst employed by Mita wanted to estimate a simple linear regression of the company's annual copier sales versus advertising dollars. Th regression results included SSE = 12593 and SSR = 87663. What is the coefficient of determination for this regression? 0.874 0.935 0.144 0.126Past class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.Stores commonly offer a cheaper unit price for large quantity purchases. Quantity 1 2 5 10 20 Unit Price $100.00 $80.00 $70.00 $50.00 $40.00 a. Use regression to find a logarithmic equation to model the data. Round the numbers in your equation to 2 decimal places. y = a + bln(z) with You b b. Use your equation to find an appropriate unit price for a customer who purchases 15 items. c. Use your equation to find an appropriate unit price for a customer who purchases 25 items. $
- 1. For a regression model y = XB + u where u is N(0, o?1), y is nx1 matrix, X is nxp matrix, B is px1 matrix and u is nx1 matrix, a. derive the estimators B using the method of least squaresA scatter plot shows data for the cost of a vintage car from a dealership (y in dollars) in the year a years since 1990. The least squares regression line is given by y-25,000 + 500z. Interpret the y intercept of the least squares regression line. Select the correct answer below O The predicted cost of a vintage car from a dealership in the year is 820.000 O The predicted cost of a vintage car from a dealershpin the year 1090 is 85,000. O The predicted cost of a vintage car from a dealershp in the year 1990 is sse. The yintercept should not be interpreted.We are interested in understanding consumption of pork in the U.S. so we run a regression of annual per capita consumption of pork on a series of independent variables using data from 1990 to 2018 and obtain the following regression results (standard errors in parenthesis) CPt = -330.3 + 49.1 In Inct − 0.34 PPt + 0.33PBt (7.40) (0.13) (0.12) R²=0.71 DW=0.94 Where CPt is the annual per capita pounds of pork consumed in the U.S. in year t InInc, is the log of per capita disposable income in the U.S. in year t PP, is the average annualized real wholesale price of pork in the U.S. in year t (in cents per pound) PB, is the average annualized real wholesale price of beef in the U.S. in year t (in cents per pound) a. Interpret the partial slope coefficients. Does the sign on the coefficients agree or disagree with your a priori assumptions? Explain b. Using a two-sided test at the 5% significant level, determine if the partial slopes are statistically significant. c. Test the presence of…
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- A multiple OLS regression of maize output (Y) on improved maize seed (X1) and fertiliser (X2) inputs (all variables in kilograms) produced the following results: Y = -342 + 12.1X1 + 46X2 se = (17.23) (0.912) (8.713) R2 = 0.861 a) Calculate the t statistics associated with the constant, improved maize seed and fertiliser coefficientsA. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables