Question:

Problem 2 A consultant was called in to assess if there is gender discrimination in professors' salaries in a small college. He considered the

simple and multiple regression models of Salary obtained from observations

on four explanatory variables for 52 randomly selected professors in a small

college, see Minitab output that follows this problem. The variables are:

Salary= academic year salary in dollars

Gender, coded 1 for female and 0 for male

Yearsinrank =number of years in current rank

Rank, coded as

Assist= 1 if assistant professor

0? otherwise

Full= 1 if full professor

0? otherwise

The left out category is Associate Professor.

Answer question below based on the Minitab output that follows after

the questions

a) Consider the graph of standardized residuals against fitted values obtained by regressing Salary on four predictors. This graph shows an unusual observation. What makes this observation unusual? What letter(s) would

be used in Unusual Observations part of Minitab output to denote this observation? Before running the regressions discussed below, the consultant removed this observation from the data set.

Questions that follow are based on the regressions obtained after an unusual observation was removed.

b) Is the simple regression model of Salary on Gender statistically significant at ? = 0?01? (state the null and alternative hypothesis and interpret

each hypothesis)

c) Interpret the coefficients in the simple regression model of Salary on Gender.

d) Consider the regression model of Salary on Assist and Full only. Carefully interpret the three coefficients in this model.

e) Consider the regression of Salary on all four predictors. Is this a statistically significant regression at ? = 0?01? (State the null and an alternative

hypothesis and your conclusion)

f) Fill in the missing information in the cell Salary/Gender in the correlation matrix.

g) Why do you think that one gets a different conclusion concerning the

statistical significance of Gender in multiple regression compared to simple

regression? Is there gender discrimination in salaries? (Discuss)

h) The consultant used the Best Subsets Regression to obtain the final

model of Salary on the four predictors. What is the consultant's "best" final

model according the best subsets regression?

QUESTION 7 According to the Central Limit Theorem. the distribution of which statistic can be approximately normal for any population distribution? What condition should the sample satisfy? ). The Central Limit Theorem approximates the sample mean Y. It is applicable when the sample size , is sufficiently large. Ob. The Central Limit Theorem approximates the sample size . It is applicable when the sample size is is not large. The Central Limit Theorem approximates the population mean j. It is applicable when the sample size or is not large. Of The Central Limit Theorem approximates the population mean a. It is applicable when the sample size of is sufficiently large. Ce, The Central Limit Theorem approximates the sample mean J. It is applicable when the sample size is is not large. Of. The Central Limit Theorem approximates the sample size n. It is applicable when the sample size , is sufficiently large.Which of the following regressions represents the weakest linear relationship between x and y? Regression 1 Regression 2 Regression 3 Regression 4. y = ar + b y = ax + b y = ar + b y = ax +b a = 13.7 a = 3.1 0 = 7.9 a = -6.3 b = 4.2 b = 15.8 b = -15.8 b =-13.6 r = 0.1735 r = 0.4662 r = 0.8971 r = -0.9644 O Regression 1 O Regression 2 Submit Answer O Regression 3 O Regression 4