data in csv format , will give later.Hill running is a long-standing Scottish tradition, dating back to 1040. The races take place at various times of year throughout Scotland. The data set (scottish_hill_races.csv) posted on Blackboard contains recent information from 90 races regarding Distance (in kilometers), Climb (in meters), Time (record time in minutes), and Sex (1 for women and 0 for men).a) Find the equation of the estimated simple linear regression function that predicts Time based on Distance.b) Plot the data with regression function found in part a). Distinguish between data points for Women and data points for Men and include a key (legend).c) Now fit the first-order regression model that predicts Time based on Distance and Sex. Provide the equation.d) Plot Time against Distance with the two separate regression functions based on Sex (one for Women and one for Men). You also need to include the equations of the two regression functions.e) Find the joint confidence intervals for the slopes with a family (Bonferroni adjusted) confidence level of 98%. Include an interpretation of each.f) Test whether Sex should be dropped from the model while Distance is retained. Include the hypotheses, test-statistic, p-value, and conclusions.g) Finally, let us consider the model that predicts Time based on Distance and Sex with interaction. Provide the equation.h) Now test whether Sex should be dropped from the model while Distance and the interaction term are retained. Include the hypotheses, test-statistic, p-value, and conclusions.i) Report the final model with Sex dropped. Does this improve upon the model found in part d)? Explain.2. Continue with the data set scottish_hill_races.csv.a) Fit the first-order regression model that predicts Time based on all potential predictors- Distance Climb, and Sex. Provide the equation.b) Construct a 95% prediction interval for the time it takes a woman to complete a 10 km race with a “climb” of 500 meters.c) Perform an exhaustive search for the “best” subsets of predictors. Which model was chosen as “best” for one predictor? Was it the one we examined in #1? How about for the “best” model with two predictors? Is it the one we examined in #1?d) Examine important criteria for the three “best” models chosen in c). Which model(s) should be included for final consideration based on them?e) Use forward stepwise selection with partial 𝐹-tests and α-to-enter= 0.01. Then use backward stepwise selection with partial 𝐹-tests and α-to-remove= 0.01. Which model is chosen as “best” in each case?f) Considering all results, which model(s) should be considered? Assess the predictive ability of the model(s) by splitting the data into training and testing (sample size 𝑛 = 40) subsets and estimating the mean squared prediction error 𝑀𝑆𝑃𝐸.g) Is there any indication of nonlinear relationships between Time and any of the quantitative predictors? Explain.h) Using basic diagnostics, is there any evidence of multicollinearity?i) Find the variance inflation factors for the quantitative predictors. Explain

Week 6 Discussion: Confidence Interval ConceptsRequired ResourcesRead/review the following resources for this activity:Textbook: Chapter 8 (All Sections)LessonMinimum of 1 scholarly sourceInitial Post InstructionsFind an example of a confidence interval in the news, scholarly source or medical journal. Summarize the article/study. Does the article/study include the sample size and the level of confidence used to create the confidence interval? Explain what the confidence interval means in context of the news article or scholarly source.