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

InstructionsInstructionsIf the question requires computation, do the calculations and then give or select the correct values using the following rule:Keep at least 4 decimal places at intermediate steps of a calculation, and round your final answer to 2 decimal places, unless otherwise noted. For example: 16.6667 would become 16.67 after rounding(In the course notes for Module 7, probabilities such .678934 are instead rounded to four decimal places, so the correct way to report the aforementioned probability is .6789)Multiple AttemptsThis test allows 2 attempts. This is attempt number 1.Force CompletionThis test can be saved and resumed later.Your answers are saved automatically.1Questions 1-4 are based on the following information: You and your friends have decided to go to The Kentucky Derby. There are 12 horses in the race. How many ways can the horses come in first, second, or third? This an example of a __________ problem? factorial combinationpermutation CPIQuestion 2Questions 1-4 are based on the following information:You and your friends have decided to go to The Kentucky Derby. There are 12 horses in the race. How many ways can the horses come in first, second, or third?What is the numeric value of N? 3 121320 none of the aboveQuestion 3Questions 1-4 are based on the following information:You and your friends have decided to go to The Kentucky Derby. There are 12 horses in the race. How many ways can the horses come in first, second, or third?What is the numeric value of r? 3 121320 none of the aboveQuestion 4Questions 1-4 are based on the following information:You and your friends have decided to go to The Kentucky Derby. There are 12 horses in the race. How many ways can the horses come in first, second, or third?What is the calculated value (solution) for this example? 3 121320 none of the aboveQuestion 5A security system uses a 2-letter password, but no letter can be used more than once. How many possible passwords are there if 5 of the letters of the alphabet can be used by the system? (Use these numbers for this question only!)For this question indicate only what the value of N is?Question 6A security system uses a 8-letter password, but no letter can be used more than once. How many possible passwords are there if 23 of the letters of the alphabet can be used by the system? (Use these numbers for this question only!)For this question indicate only what the value of r is?Question 7A security system uses a four-letter password, but no letter can be used more than once. How many possible passwords are there if 26 of the letters of the alphabet can be used by the system? (Use these numbers for this question only!Question 8How many ways are there to select a subcommittee of 7 members from among a committee of 38? (Use these numbers for this question only!)Question 9You have 12 friends with whom you like to play golf. However, the golf cart only seats 4 people. Since you will take up one seat, you can only play with 3 friends at one time. How many different groups of golfers can you have?This an example of CombinationPermutationInverted statistical combinationInverted statistical permutationQuestion 10You have 71 friends with whom you like to play golf. However, the golf cart only seats 4 people. Since you will take up one seat, you can only play with 3 friends at one time. How many different groups of golfers can you have? (Use these numbers for this question only!)What is the value of N in this example?Question 11You and your friends have decided to go to the horse races. There are 10 horses in the first race. How many different ways can the horses come in first, second, and third?Question 126! Is equal to what number?30120360720Question 13Which of the following statements is a true statement?With a combination, order matters.r represents the total possible number of objects being counted.With a permutation, order matters.With a permutation, order does not matter.With both permutation and combination, order does not matter.Question 14Which statement below is false regarding the CPI?The CPI is the most common measure of change in the cost of living in the United States.The CPI is based on a variable market basket price index.The CPI is a common measure of inflation.The CPI measures the cost of a market basket of goods and services that represent the typical purchases of urban households.Question 15Using 1995 as the base period, the price index for cars is now 140. What does this index number mean?The price of cars has decreased 40% since 1995.The price of cars has increased 40% since 1995.The price of cars has increased 140% since 1995.The current price of cars is within $140 of the 1995 price.Question 16A _________ economic indicator is one whose changes precede changes in the economy.LeadingCoincidenceLaggingVangardQuestion 17One criticism of the CPI is that the market basket used in the CPI may not reflect current spending priorities. Which of the following is an example of this?Personal computers were less powerful in 1982-1984.Cell phones are more commonly purchased today than in 1993-1995.Using extreme couponing methods, a family can save hundreds of dollars a month.Goods cost more in Alaska and Hawaii due to transportation costs.Question 18The CPI's at the start of each decade from 1950 to 2005 were: What was the rate of inflation for the 1960s, as measured by the percentage change in the CPI?9.2%22.8%23.7%31.1%Question 19The CPI's at the start of each decade from 1950 to 2005 were: What was the rate of inflation for the 1980s, as measured by the percentage change in the CPI?37.0%48.3%58.6%112.4%Question 20Which of the following is not one of the 8 major categories of the CPI, as of 1998?ApparelDairy and related productsMedical careRecreationQuestion 21If rent for a particular apartment was $477/month in 1980 (CPI = 82.4), what would be the comparable rent in 1990 (CPI 130.7)? Round your answer to the nearest cent (i.e. two decimal places). Only enter the number, not the dollar sign ($). Question 22What was the original base year for the CPI?1899191319821989Question 23The Consumer Price IndexIs representative of the typical family budget in the Midwest.Was originally developed to determine salary adjustments.Is updated every three years to reflect inflation.Was last updated in 1981.

Congruent TrianglesYou have learned five ways to prove that triangles are congruent: SSS, SAS, ASA, AAS, and HL. You are going to model these theorems with string and a protractor. Example: Recreate the following triangle using HL. HL requires a right angle, so use a protractor to create a right angle.Choose a leg of the original right triangle. Cut a piece of string the length of that leg.Lay the string along the corresponding leg of the right angle that you drew in Step 1 and make the leg the same length as the string by either extending the side or erasing part of the side.Cut a piece of string the length of the hypotenuse of the original right triangle.Lay one end of the string at the top of the leg that you created in Step 3. Make the other end of the string intersect the other side of the right angle, forming a triangle. Trace the string. Make the bottom leg of the triangle the correct length by either extending the side or erasing part of the side.You’ve now copied the triangle using HL.Proving Triangles CongruentComplete the following table to summarize the different ways to prove triangles congruent.Postulate/TheoremWhat It SaysRequired InformationPictureSSSIf the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.three sets of congruent sidesSASASAAASHLYou will turn in the chart above.Recreating the Original TriangleYou will be using the following original triangle in the following activity. With a ruler, measure the sides of the original triangle to the nearest millimeter. Write down the length of each side in your math journal.With a protractor, measure the angles of the original triangle to the nearest degree. Write down the measure of each angle in your math journal. SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor.Answer the following questions in your math journal:Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures?SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side.Answer the following questions in your math journal:Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length?ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them.Answer the following questions in your math journal:Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle?Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?You will need to submit the following:the answers to questions 1–6 aboveyour re-drawn triangles with the pieces of string that you cut taped to each drawingYou will need to submit the following:the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem, written in your own wordsAt the end of the assignment, you will need to submit the following:a chart summarizing all of the postulates and theorems that can be used to prove two triangles congruentthe answers to six questions about recreating a triangle using a protractor, string, and the SSS, SAS, and ASA Congruence Postulatesthree drawings of recreated triangles, with the string used to create the drawings taped to the appropriate drawinga description of the steps that you would follow to recreate a triangle using a protractor, a string, and the AAS Congruence Theorem, written in your own words