Exam 14: Inference About Simple Regression

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. -What is the estimated change in the average selling price of a house for an increase in house size of 100 square feet?

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 is the equation of the least squares regression line?

Use the following information for questions: A regression line relating y =student's height (inches) to x = father's height (inches) for n = 70 college males is $\hat{y}$ = 15 + 0.8 x. -What is the estimated height of a son whose father's height is 70 inches?

Use the following information for questions: A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested: H₀: $β_1 = 0$ H_a: $β_1 ≠ 0$ -What is the p-value for testing the following hypothesis about the correlation coefficient

Use the following information for questions: The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894. -What is the proportion of variation in weight that is explained by the linear relationship with height?

Consider the following plot of residuals versus x for a regression analysis. Which statement is not true about the regression model?

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. -Max is 70 inches tall. If a 95% prediction interval for his foot length were calculated, the width of this interval would _______ with respect to the interval from question 99.

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. -Calculate a 95% confidence interval for the average foot length for all college men who are 70 inches tall. Descriptive statistics for the two variables are provided below. Use the mean to obtain $\overline{x}$ and note that = 289.87

Shown below is a scatterplot of y versus x. Which choice is most likely to be the approximate value of r², the proportion of variation in y explained by the linear relationship with x?

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. -Identify the response and the explanatory variable.

Use the following information for questions: A regression line relating y =grade point average to x = hours studied per week is estimated using data for n = 5 students. The estimated slope is b₁ = 0.02. The standard error of the slope is s.e.(b₁) = 0.01. -What is a 95% confidence interval for $\beta$ ₁ , the population slope ?

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. -Some of the regression output is provided below. Give the value of $r^2$ and interpret it in the context of the problem.

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. -What is the correlation between height and foot length?

Use the following information for questions: A regression line that relates y = hand span (cm) and x = height (inches) is $\hat{y}$ = -1 + 0.3 x. The sample size was n = 5 adults. The standard deviation of the regression is s = 1 cm. For height = 60 inches, the standard error of the fit is s.e.(fit) = 1 cm. -What is a 90% prediction interval for the hand span of a person whose height is 60 inches?

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. -Give the least square regression equation for predicting price from house size.

Use the following information for questions: A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 - 2(Latitude). -Suppose that the latitudes of two cities differ by 10. What is the estimated difference in the average January temperatures in the two cities?

Use the following information for questions: A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 - 2(Latitude). -Estimate the average January temperature for a city at Latitude = 45.

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. -Write the null and alternative hypotheses for assessing if there is a significant positive linear relationship between price and size for the population of all houses in your town.

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 slope of the regression line is ______

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 would the 95% confidence interval for the average fuel efficiency for all cars that hold 18 gallons of fuel compare to the interval calculated in question 89?