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- Suppose that a researcher, using data on class size (CS) and average test scores from 102 third-grade classes, estimates the OLS regression TestScore=515.196+ (-5.7618)x CS, R² = 0.06, SER=11.4. A classroom has 23 students. The regression's prediction for that classroom's average test score is (Round your response to two decimal places.) Last year a classroom had 20 students, and this year it has 24 students. The regression's prediction for the change in the classroom average test score is (Round your response to two decimal places.) The sample average class size across the 102 classrooms is 21.19. The sample average of the test scores across the 102 classrooms is (Hint: Review the formulas for the OLS estimators.) (Round your response to two decimal places.)Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by 20² Var(et) 2 – α Where o² is the variance of individual observation and a is the parameter in the ES method. =When using a regression line, the sum of the residuals should be equal to zero negative maximized positive In a sense, the standard error can be thought of as a standard deviation of the residuals. True False
- Q1/ A sample of 6 beams was selected the value of their deflections (x variable) and their weight is demonstrated in the following table. Find the regression equation and what is the predicted weight when deflection is Sequence your name in the list. Serial no. Def. (x) Weight (y) 1 7 12 8 8 12 4 5 10 5 6 11 9 13Tom has been gathering data concerning the cost of a spa treatment, y', during the before Valentine's Day. The only independent variable that he has considered is the number of minutes, "x," in the treatment. Suppose Tom collects data on the relationship between the number of minutes in a treatment and the resulting cost of we the treatment. Tom finds that the correlation between cost and number of minutes is strong and positive. Therefore, he has performed a linear regression analysis on his data. His results are that the constant "a" is 35, and the coefficient "b1" for the independent variable is 1.3. Which of the following is the correct linear regression equation that would allow Tom to predict the cost of a spa treatment given the number of minutes? Oy = 78x + 35 Oy' = 1.3x + 35 %3D Oy = 78x - 1.3 %3D OY = -1.3x - 35There is a relationship between the following variables as y = 1 / (a * x ^ b) (x ^ b: means x over b). a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation. x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10 x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10
- I have modeled adult worker's salaries based upon their work experience. After surveying 200 adults about their salary and years in the workforce, I have found the following model: y=12000+5000*x where y is the predicted salary and x is the years in the labor force. R^2 = 0.63. What is the correlation for this model? (correlation between salary and years in the labor force)? a. 0 b. 0.79 c. 0.63 d. 0.50 e. 1** Based on the regression results, answer the following questions ** A sample of data is collected (from 1999 and 2000) concerning the compensation of the executives (compensation is measured in 1000’s of $’s) of a number of public companies along with other firm-specific data. The dependent variable is total compensation, CEOANN is a dummy variable =1 for an individual who is a CEO and =0 for individuals who are not CEO’s, EMPL is total employees, MKTVAL is the natural logarithm of the market value of the firm, EPSIN is earnings per share, YEAR is a dummy variable = 1 for the year 2000 and =0 for year 1999, and ASSETS is the natural logarithm of the total assets of the company. Based on the regression results, answer the following questions b) What is the estimated regression equation? c) What percentage of the variation in income in explained by the regressors? d) What is the standard error of the error term in the regression equation?If you have a b of 0.56 in a regression equation, what does this mean? For every one-unit increase in x, you get an increase of 0.56 in y r = .31 On average, the variability of real scores around the regression line is 0.56 For every 1 standard deviation increase in x, you get an increase of 0.56 standard deviations in y
- The individual residual scores from a sample of participants regarding the difference between the predicted Y values from a regression equation and the actual Y from the data are provided here. Y - Ŷ = 3,8,1,2,2. What is the value for the standard error of estimate?An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.