Please use R or R Studio for the following questions.

1.1. Access the Salaries dataset by using the code: library(car); library(carData); data(Salaries)

Plot salary vs. years since PhD. What's your interpretation?

1.2. What is the correlation for salary vs. years since PhD? Is it statistically significant?

1.3. What is the correlation for salary vs. years of service? Is it statistically significant?

1.4. Draw a visualization of all bivariate relationships.

1.5. Check skewness of "salary" variable that is a dependent variable of your regression model. Should it be transformed? If so, how?

1.6. Run a linear regression model that predicts salary (DV: salary) based on the number of service years (IV: yrs.service). And interpret your results of the above regression analysis. Hint: Focus on (1) estimated coefficient and (2) R-squared.

1.7. If a new professor who has 10-year experience of service joins ISU next semester, then your prediction based on the model of her/his salary is...?

1.8. Run a linear regression model (model.1) that predicts salary (DV: salary) based on the following independent variables, yrs.since.phd, yrs.service, sex, rank, discipline. And interpret your results of the above regression analysis. Hint: Focus on (1) estimated coefficients, (2) R-squared, and (3) Adjusted R-squared.

1.9. Check "multicollinearity" in the model.1 by using Variance Inflation Factor (VIF).

1.10. Run a linear regression model (model.2) by dropping a variable whose VIF or GVIF is the highest from model.1. And interpret your results of the above regression analysis. Hint: Focus on (1) estimated coefficients, (2) R-squared, and (3) Adjusted R-squared.

1.11. Compare the two models (i.e., model.1 and model.2) by using (1) R-squared & Adjusted R-squared, (2) visualization, and (3) formal statistical test.

Chi-square Goodness of Fit Problem OBSERVED VALUES Observed Expected Generation % of SmartPhone Users % of SmartPhone in County Users in Nation GI Generation 2% 6% Mature 9% 7% Baby Boomers 72% 79% Generation X 91% 96% Generation Y/Millennium 99% 97% Generation Z/Boomlets 99% 98%Refer to the "Chi-square Goodness of Fit Problem DATA" Excel file. Perform a Chi-square Goodness of Fit test to determine if the statistical distribution of the % of smartphone users in the county is the same as it is in the Nation. Specifically for this problem, perform the following: 1. Evaluate the information in the table. Without performing any analysis, does it appear that the statistical distribution of the $ of smartphone users in the county Is the same as it is in the Nation? Why or why not? 2. State the Null and Alternative Hypotheses for a Chi-square Goodness of Fit test. 1. Determine the Chi-square (i.e., X crit) Critical value (hint: use Excel's =CHISQ.INV.RT function). Assume a statistical significance of 0.05. 4. Compute the Chi-square (I.e., X-stat) Test Statistic. 5. Determine the p-value (hint: use Excel's = CHIDIST function), 6. Should the Null Hypothesis be rejected? Why or why not? 7. Briefly summarize your conclusions of the Chi-square Goodness of Fit test. Assume you are explaining it to someone who is not familiar with this type of statistical test.2. + 0/2 points Previous Answers MendStat14 8.E.037. & M A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A r sample of 500 registrations are selected from a Department of Motor Vehicles database, and 92 are classified as sports ut vehicles. (a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your ar to three decimal places.) to (b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? ( There are two answers. Select all that apply.) decrease the sample size n O decrease Za/2 by increasing the confidence coefficient O increase the sample size n increase z /2 by increasing the confidence coefficient decrease z /2 by decreasing the confidence coefficient increase za/2 by decreasing the confidence coefficient O conduct a non-random sample You may need to use the appropriate appendix table or technology to answer this question. Need Help? Read It Talk to a Tutor