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Use the InsurancePremium sheet. Develop a multiple linear regression model to predict the monthly car insurance premium based on the age of the driver and the type of car (sedan, SUV, or sports car). Use sedan as the baseline. What is the estimated monthly insurance premium for a 26-year-old driver with a sports car? Please round your answer to the nearest integer.

[Continued] Use the Enrollment sheet. Based on your regression model from the previous question, what is the predicted enrollment in Year 18? One decimal place.

[Continued] Use the Enrollment sheet. Based on your regression model from the previous question, what is the predicted enrollment in Year 18? One decimal place.

At the Nevermore Library, study sessions average 52 minutes with a standard deviation of 8 minutes. The session duration follows a normal distribution. Using the empirical rule, what percentage of sessions last between 36 minutes and 76 minutes? Please answer in one decimal place without the % mark.

Suppose we run the following linear regression model: BloodPressure = b0 + b1*BodyWeight + b2*PotassiumIntake, where BodyWeight is measured in lbs, and PotassiumIntake is the average daily potassium consumption (mg/day).   We find that b1​ is positive (higher body weight increases blood pressure) and b2​ is positive (higher potassium intake raises  blood pressure). Assume that BodyWeight and PotassiumIntake are negatively correlated (individuals who eat more potassium-rich foods like fruits and vegetables tend to have lower body weight). If PotassiumIntake were omitted from the model and only BodyWeight were included, would you expect the estimated coefficient on BodyWeight to be larger or smaller than the b1​ estimated when PotassiumIntake is included? Explain briefly. Note: Use your understanding of regression analysis to answer this question. When answering, be sure to first state whether you expect the coefficient to become larger or smaller, and then explain why in your own words.

If all forecast errors are negative, which of the following statements must be true?

In regression analysis, we use the t-test’s p-value to determine whether the coefficient on a variable is statistically different from ________.

Suppose we run the following linear regression model: BloodPressure = b0 + b1*BodyWeight + b2*PotassiumIntake, where BodyWeight is measured in lbs, and PotassiumIntake is the average daily potassium consumption (mg/day).   We find that b1​ is positive (higher body weight increases blood pressure) and b2​ is positive (higher potassium intake raises  blood pressure). Assume that BodyWeight and PotassiumIntake are negatively correlated (individuals who eat more potassium-rich foods like fruits and vegetables tend to have lower body weight). If PotassiumIntake were omitted from the model and only BodyWeight were included, would you expect the estimated coefficient on BodyWeight to be larger or smaller than the b1​ estimated when PotassiumIntake is included? Explain briefly. Note: Use your understanding of regression analysis to answer this question. When answering, be sure to first state whether you expect the coefficient to become larger or smaller, and then explain why in your own words.

At the Nevermore Library, study sessions average 52 minutes with a standard deviation of 8 minutes. The session duration follows a normal distribution. Using the empirical rule, what percentage of sessions last between 36 minutes and 76 minutes? Please answer in one decimal place without the % mark.

Use the Probit sheet. The Department of Health Services aims to predict whether an individual will receive an annual flu shot using a probit regression model based on community health survey data. As predictors, the model considers age (in years), income (in thousands), health insurance coverage (1 if insured, 0 otherwise), and length of residence (measured by the number of years the person has lived in their current zip code). The Probit sheet contains the descriptive statistics and probit regression results. Based on these results, interpret the coefficient (B) on “income”. (Hint: Use the term “z-score in favor of receiving a flu shot”)