Exam 14: Inference About Simple Regression

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 a 90% confidence interval for $\beta$ ₁? (Table A.2 or its equivalent needed.)

Use the following information for questions: Grades for a random sample of students who have taken statistics from a certain professor over the past 20 year were used to estimate the relationship between y = grade on the final exam and x = average exam score (for the three exams given during the term). -The two values used to determine r² are

Use the following information for questions: A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8. -For a student with a right hand span of 26 cm, what is the estimated left hand span?

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. -Use the empirical rule to find an interval that describes the weights of approximately 95% of male college students who are 70 inches tall.

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 a 90% confidence interval for $\beta$ ₁? (Table A.2 or its equivalent needed.)

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). -How does the estimated temperature change when latitude is increased by one?

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. -If the son's actual height is 68 inches, what is the value of the residual?

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). -Based on the equation, what can be said about the association between temperature and latitude in the sample?

The slope of the regression line tells us

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 observed value of the test statistic and the corresponding p-value?

Use the following information for questions: Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by Ideal weight = 53 + 0.7 *actual weight -In this context, the slope of +0.7 indicates that

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 regarding the form and direction shown in Plot A.

Use the following information for questions: Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by Ideal weight = 53 + 0.7 *actual weight -If a man weighs 200 pounds but his ideal weight is 210 pounds, then his residual is

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 the value of the p-value for the test in question 62?

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 the value of the test statistic for the following hypothesis test about $β_1$ , the population slope? H₀: $β_1 = 0$ H_a: $β_1 ≠ 0$

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. -To assess if there is a significant linear relationship between fuel efficiency and fuel capacity, what is the observed value of the test statistic and the corresponding p-value?

For the regression line $\hat{y}$ = b₀ + b₁ x, explain what the values b₀ and b₁ represent.

Which choice is not an appropriate term for the x variable in a regression equation?

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. -What is the equation of the least squares regression line for predicting fuel efficiency from fuel capacity?

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% confidence interval for the mean hand span of people who are 60 inches tall?