Please help answer two of the questions below. Thank you.

Suppose we decide to run an experiment to investigate the relation ship between Age and Fitness level of Toronto residents. We dene Fitness level to be the time it takes to run 3 laps on a standard running track. We categorize Age into 3 levels: 13-30 years old, 31-50 years old, and 51-70 years old. We recruit 10 random individuals for each age group and record the time it takes to run these 3 laps. We are ultimately interested in learning whether the average Fitness level is different across age groups. a How might a linear regression model be used to determine if the average Fitness level is different across only two of the age groups? 0 How would we write out this model relating Fitness levels of individuals to the average Fitness level in an age group. while accounting for random variation between individuals in the same age group? 0 What do the coefficients represent? 0 What testis} could you use to determine if the average Fitness level is different across only two of the age groups? You can consider hypothesis tests outside of regression as well. 0 What sources of variation could explain the variability in the Fitness level we observe in our sample? . How would we modify the linear regression model to compare the average Fitness level across all three age groups? 0 What does this model look like and what would the coefcients represent? 0 What hypothesis are we testing if we're interested in whether the Fitness level on average is different across all three groups? Would we use the same test as when comparing across only two groups? Why or why not? 0 What assumptions would we need to satisfy for us to use a linear regression model to perform this test (consider both cases where we are comparing two age groups and three age groups)? 0 How might you detect violations of these assumptions by simply plotting your data or by examining how it was collected? 0 If assumptions are violated. what will happen to the conclusions of our hypothesis tests