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- Suppose that given a particular dataset of (x, y) pairs, the correlation coef- ficient (r) of the least-squares line is -.98. What conclusion can we draw from this 19. information? A. X and Y have a strong linear correlation B. X and Y have a moderate linear correlation C. X and Y have a weak linear correlation D. X and Y are not linearly correlated E. None of the above 20. Given the following summary data from a sample of size 9, what is the slope of the least-squares line for x and y? E; = 24 Σ-70.50 Σ- - 902.25 Ev = 11, 626.75 Yi = 312.5 %3D A. .089 В. 13.150 C. 13.052 D. 10.603 E. None of the aboveSuppose that average worker productivity at manufacturing firms (avgprod) depends on two factors, average hours of training (avgtrain) and average worker ability (avgabil): augprod = Bo+Biavgtrain + B2avgabil + u. Assume that this regression satisfies assumptions MLR 1-4. If grants have been given to firms whose workers have less than average ability so that avgtrain and avgabil are negatively correlated. Which is the following is true regarding the estimated coefficient on avgtrain in the following regression avgprod=Bo + B₁avgtrain + u. Ounblased blased upwards biased downwards undetermined.Suppose that @, and ô, are unbiased estimators of the parameter 0 and that V@,) = 15 and V(@2) = 4. What is the relative efficiency of the two estimators?
- Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual model…Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERSSuppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 12 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.85, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 85000 and the sum of squared errors (SSE) is 15000. From this information, what is SSE/SST? (a) .2 (b) .13 (c) NONE OF THE OTHERS (d) .15 (e) .25
- Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.8, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 80000 and the sum of squared errors is (SSE) 20000. From this information, what is the value of the hypothesis test statistic for evidence that the true value of the coefficient of the second explanatory unknown exceeds 5? (a) 4 (b) 3…0. In a statistical study, it is found that variables z and y are correlated as follows. Find the least squares regression line in this model.It is known that a natural law obeys the quadratic relationship y = ax-. Whatis the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly atrandom from the domain [0, 1]?
- Suppose the least squares regression line for predicting weight (in pounds) from height (in inches) is given by Weight= -110+3.5*(height) Which of the following statements is correct? l. A person who is 61 inches tall will weigh 103.5 pounds ll. For each additional inch of height, weight will decrease on average by 3.5 pounds. lll. There is a negative linear relationship between height and weight. a) l and lll only b) l and ll only c) ll only d) l only e) ll and lll onlyExample 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 9. 8. 8 7 6. 10 4 7 Marks in 2nd Test (Y) 8 7 10 8 10 9. 8 6. (a) Find the least square regression line of Y on X. / (b) Test the hypothesis that marks in the two tests are linearly related.Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 16 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 45/62, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 34000. From this information, what is the critical value needed to calculate the margin of error for a 95 percent confidence interval for one of the model coefficients? (a) 2.069 (b) 2.110 (c)…
