Exam 14: Inference About Simple Regression

Use the following information for questions: Can an athlete's cardiovascular fitness (as measured by time to exhaustion on a treadmill) help to predict the athlete's performance in a 20k ski race? To address this question the time to exhaustion on a treadmill (minutes) and the time to complete a 20k ski race (minutes) were recorded for a sample of 11 athletes. The researcher knows he is to examine the data graphically and to check various assumptions before assessing significance of the regression equation. Consider the following two plots. -Give an appropriate summary for what Plot B shows. Be sure your answer includes the assumption or data condition being assessed.

Use the following information for questions: A car salesman is curious if he can predict the fuel efficiency of a car (in MPG) if he knows the fuel capacity of the car (in gallons). He collects data on a variety of makes and models of cars. The scatterplot shows that a linear model is appropriate. SPSS output is provided below. -How much would you expect fuel efficiency to change for every 1-gallon increase in fuel capacity? Include the units in your answer.

Use the following information for questions: Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested: H₀: $β_1=0$ H_a: $β_1≠0$ -What is the value of the t-statistic for testing the hypotheses?

Use the following information for questions: A car salesman is curious if he can predict the fuel efficiency of a car (in MPG) if he knows the fuel capacity of the car (in gallons). He collects data on a variety of makes and models of cars. The scatterplot shows that a linear model is appropriate. SPSS output is provided below. -Suppose Bob's car holds 18 gallons of fuel. Based on the least squares regression line, what is the predicted fuel efficiency for Bob's car?

Use the following information for questions: A consumer agency employee has been researching and testing food products for months. He is convinced that the dimensions of the packaging used for dry goods (crackers, cookies, cereal, etc) all satisfy a certain ratio. He will try to model the relationship between the minimum width of a box and the height of the box, to see if he can predict the height of the box from the minimum width (both measured in inches). Data is collected on 24 randomly selected products. The scatterplot shows that a linear model is appropriate. (Partial) SPSS output is provided below. -What are the response and explanatory variables in this study?

Use the following information for questions: A consumer agency employee has been researching and testing food products for months. He is convinced that the dimensions of the packaging used for dry goods (crackers, cookies, cereal, etc) all satisfy a certain ratio. He will try to model the relationship between the minimum width of a box and the height of the box, to see if he can predict the height of the box from the minimum width (both measured in inches). Data is collected on 24 randomly selected products. The scatterplot shows that a linear model is appropriate. (Partial) SPSS output is provided below. -Is the linear relationship between minimum width and height statistically significant at the 5% significance level? Include the p-value you used to answer this question

Use the following information for questions: A car salesman is curious if he can predict the fuel efficiency of a car (in MPG) if he knows the fuel capacity of the car (in gallons). He collects data on a variety of makes and models of cars. The scatterplot shows that a linear model is appropriate. SPSS output is provided below. -Suppose Bob's car holds 18 gallons of fuel and has a fuel efficiency of 28 MPG. Based on the least squares regression line, what is the residual for Bob's car?

Use the following information for questions: The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x -The estimated ideal weight for a women who weighs 118 pounds is ______

Use the following information for questions: The heights (in inches) and foot lengths (in centimeters) of 32 college men were used to develop a model for the relationship between height and foot length. The scatterplot shows that a linear model is appropriate. SPSS output is provided below. -Give the equation of the least squares regression line for predicting foot length from height.

Use the following information for questions: Can an athlete's cardiovascular fitness (as measured by time to exhaustion on a treadmill) help to predict the athlete's performance in a 20k ski race? To address this question the time to exhaustion on a treadmill (minutes) and the time to complete a 20k ski race (minutes) were recorded for a sample of 11 athletes. The researcher hypothesizes that there would be an inverse linear relationship, that is, the longer the time to exhaustion, the faster the athlete's time in the 20k ski race, on average. The data were used to provide the following output. -What is the least squares regression equation for predicting the race time based on the skier's treadmill exhaustion time?

Use the following information for questions: A linear regression analysis of the relationship between y = grade point average and x = hours studied per week is done using data from n = 10 students. The error sum of squares is SSE = 100 and the total sum of squares is SSTO = 900. -What is the value of r², the proportion of variation in grade point average explained by the linear relationship with x = hours studied per week?

Use the following information for questions: Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested: H₀: $β_1=0$ H_a: $β_1≠0$ -What is the p-value for the test? (Table A.3 or its equivalent needed.)

Use the following information for questions: A regression line relating y = hours of sleep the previous day to x =hours studied the previous day is estimated using data from n = 10 students. The estimated slope b₁ = -0.30. The standard error of the slope is s.e.(b₁) = 0.20. -What is the value of the p-value for the test in question 59?

Use the following information for questions: The heights (in inches) and foot lengths (in centimeters) of 32 college men were used to develop a model for the relationship between height and foot length. The scatterplot shows that a linear model is appropriate. SPSS output is provided below. -To assess if there is a significant linear relationship between height and foot length, the hypotheses to be tested are H₀: $\beta$ ₁ = 0 versus H_a: $\beta$ ₁ $\neq$ 0. What is the correct conclusion at the 1% significance level?

Use the following information for questions: Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size. -The observed selling price for that house was $200,000. Compute the residual value.