please explain the answer. thank you. 21. Is there a relationship between the ra

Question

please explain the answer. thank you.

21. Is there a relationship between the raises University administrators receive and their performance on the job? A faculty group wants to determine whether job rating (r) is a useful linear predictor of raise (y). Consequently, the group considered the linear regression model: E(y) + Ax. The faculty group obtained the following prediction equation: y 14,000-2000x Which of the following statements about the model E (y) = + Ax is correct? a) The model hypothesizes that the raises for the administrators fall in a perfect straight line b) The model hypothesizes a line of means; as rating (x) increases, the mean raise Ey) moves up or down along a straight line. c) The model hypothesizes that knowing an administrator's rating (r) will determine exactly the d) The model hypothesizes that, on average, administrators make more money than professors. 22. Continuing from the previous problem, which interpretation about the prediction equation is correct? administrator's raise (y). a) Higher raises for administrators cause administrators to have lower job ratings If an administrator's job rating is higher than a professor's, the administrator will earn a larger raise than the professor b) c) When a typical administrator's job rating improves by one, the administrator's salary decreases biy d) $2,000 on average If an individual administrator's job rating falls by one, this administrator will have a $2,000 decrease in his/her sal 23. An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT was created from a set of 25 data points. Which of the following is not an assumption required for the simple linear regression analysis to be valid? a) SALARY is independent of GMAT b) The errors of predicting SALARY are normally distributed. c) The errors of predicting SALARY have a mean of 0 d) The errors of predicting SALARY have a variance that is constant for any given value of GMAT 24. The dean of the Business School at a small Florida college wishes to determine whether the grade -point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA (x) and starting salary y, in $thousands) for each graduate were used to fit the model E (y) = Ax. The results of the simple linear regression are provided below SSxy = 5.15 SSyy = 15.17 SSxx = 1.87 SSE = 1.0075 = 4.25 + 2.75x Compute an estimate of o, the standard deviation of the random error term. a) 1.0075 b) 0.689 c) 0.048 d) 0.219

Explanation / Answer

1. Statement (c) is true

As ratings (x) is the predictor variable

And raise ( y) is the explanatory variable

So we get the estimated value of y if we know x

2.(c) is correct

As we see that slope of the equation is -2000

So for unit rise in x there is decrease in y ( negative slope) on an average by 2000

3. Answer is (a)

As in the regression equation salary is the dependent (expanatory) variable here and gmat score is the predictor variable

Also in regression the distribution of error is normally distributed with mean 0 and variance 1so b, c, d are valid assumptions

4.the sd of the random error is given by sse = 1.0075

So answer is (a)

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