Exam 14: Inference for Regression

Use the following information to answer the question. A high school boys cross country coach performs a regression to predict the finish times of runners in the 10k event from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Regression Analysis: Training versus Finish Time The regression equation is finish time $=65.84-0.15$ training minutes Predicted Values: value Pred. Y s.e. (Pred. y) 95\% C.I. 95\% P.I. 180 38.84 1.44112 (34.73,42.95) (31.13,46.55) -The coach wants to predict the finish time of his top runner who trained for 180 minutes the previous week. Should the coach use a confidence interval or a prediction interval?

Use the following information to answer the question. A high school girls cross country coach performs a regression to predict the finish times of runners in the 10k event from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Regression Analysis: Training versus Finish Time The regression equation is finish time $= 69.71 - 0.13$ training minutes Predicted Values: X value Pred. Y s.e. (Pred. y) 95\% C.I. 95\% P.I. 145 50.86 1.82543 (46.09,55.63) (44.85,56.87) -The coach wants to predict the finish time of his top runner who trained for 145 minutes the previous week. Should the coach use a confidence interval or a prediction interval?

Researchers studying the relationship between the number of fat grams and the net weight in ounces of a fun size package of peanut M & M's believe that the deterministic component of the relationship is a straight line. A scatterplot shows that even though the general trend is linear, the points do not fall exactly on a straight line. Describe two factors that might account for the random component of this regression model.

Use the following information to answer the question. A humanities professor is interesting in learning whether there is a positive association between average online homework scores and the final class average in an online humanities course. The computer output below shows the results from a regression model in which the final class average was predicted by the average online homework score. Assume that the conditions of the linear regression model are satisfied. LinRegTTest for y=a+bx \beta>0 a=-11.15986949 t=8.285803594 b=1.111745514 p=2.0898031E-4 s=4.349532611 df=124 r=.9654613007 -Choose the correct null and alternative hypothesis to test whether there is an association between final class average and average online homework scores.

Choose the statement(s) that are not true about the estimators for slope and intercept of a regression line when the conditions of the linear model hold. If each statement is true choose (d).

Choose the condition of the linear regression model that cannot by verified by examining the residuals. Choose (d) if all the conditions given can be verified by examining the residuals.

Choose the correct decision regarding the null hypothesis and the correct conclusion. State your conclusion using a significance level of 5%.

Use the following information to answer the question. An engineer is interested in learning whether there is an association between temperature (°F) and the strength of an automotive plastic cup holder which is measured by finding the pounds per square inch (psi) it takes to break the cup holder. The computer output below shows the results from a regression model in which the breaking point in psi was predicted by the temperature. Assume that the conditions of the linear regression model are satisfied. LinRegTTest for y=a+bx \beta>0 a=10.06846186 t=5.9838909 b=.2252509467 p=9.3423882E-4 s=2.595293293 df=119 r=.9367346759 -What is the observed value of the test statistic and the p-value? Round to the nearest thousandth.

Use the following information to answer the question. Below is the scatterplot showing the association between miles driven in a semi truck (x), and the amount of tread wear on the tires (y). The residual plot of the data is also shown along with a QQ plot of the residuals. -Choose the statement that best describes whether the condition for normality of errors does or does not hold for the linear regression model.

Environmental biologists studying the relationship between the number of owls in a forested region and the number of field mice in the region believe that the deterministic component of the Relationship is a straight line. A scatterplot shows that even though the general trend is linear, the Points do not fall exactly on a straight line. Which of the following factors might account for the Random component of this regression model?

Use the following information to answer the question. A high school boys cross country coach performs a regression to predict the finish times of runners in the 10k event from the number of minutes of training in the previous week. The output is shown below. Assume that the conditions of the linear regression model hold. Regression Analysis: Training versus Finish Time The regression equation is finish time $=65.84-0.15$ training minutes $\text { Predicted Values: }$ X value Pred. Y s.e. (Pred. y) 95\% C.I. 95\% P.I. 180 38.84 1.44112 (34.73,42.95) (31.13,46.55) -Suppose the coach's top runner trained for 180 minutes the previous week. If this runner participates in the 10k event, what is the coach's expected finish time for this runner? Can he be Reasonably confident that this runner will beat the previous season's record of 43 minutes? The previous season's record of 43 minutes because the interval contains the value of 43 Minutes.

Use the following information to answer the question. A random sample of 30 married couples were asked to report the height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model are satisfied. Regression Analysis: Spouse versus Parent The regression equation is spouse =48.40+0.25 parent Predictor: Constant Predictor: Parent Parameter Estimate: 48.398 Parameter Estimate: 0.247 Standard Error: 39.695 Standard Error: 0.566 T-statistic: 1.219 T-statistic: 0.437 p-value: 0.277 p-value: 0.680 =7.794899045 R-sq =0.036858791=0.1919864344 -If the intercept was 0 and the slope was 1, what would that say about the association?

Use the following information to answer the question. Below is the scatterplot showing the association between miles driven in a semi truck (x), and the amount of tread wear on the tires (y). The residual plot of the data is also shown along with a QQ plot of the residuals. -Based on the plots provided, choose the statement that best describes whether the condition for constant standard deviation does or does not hold for the linear regression model.

Use the following information to answer the question. A random sample of 30 couples who were also new home owners were asked to report the cost of their first house and their combined age when they married. The output of a regression analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are satisfied. Regression Analysis: Combined age versus home cost The regression equation is home cost =73.74+2122.75 combined age Predictor: Constant Predictor: Combined Age Parameter Estimate: 73.74 Parameter Estimate: 2122.75 Standard Error: 24.655 Standard Error: 4.814 T-statistic: 0.003 T-statistic: 4.882 p-value: 0.998 p-value: 0.008 =19837.70325-=0.8562890509 =0.9253588768 -What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context.

Use the following information to answer the question. Below is the scatterplot showing the association between raw material (in tons) put into an injection molding machine each day $( x )$ , and the amount of scrap plastic (in tons) that is collected from the machine every 4 weeks $( y )$ . The residual plot of the data is also shown along with a QQ plot of the residuals. -Choose the statement that best describes whether the condition for constant standard deviation does or does not hold for the linear regression model.

Which of the following statements is not true about prediction intervals?

Use the following information to answer the question. An engineer is interested in learning whether there is an association between temperature (°F) and the strength of an automotive plastic cup holder which is measured by finding the pounds per square inch (psi) it takes to break the cup holder. The computer output below shows the results from a regression model in which the breaking point in psi was predicted by the temperature. Assume that the conditions of the linear regression model are satisfied. LinRegTTest for y=a+bx \beta>0 a=10.06846186 t=5.9838909 b=.2252509467 p=9.3423882E-4 s=2.595293293 df=119 r=.9367346759 -State the null and alternative hypothesis to test whether there is an association between temperature and break strength two different ways.

Use the following information to answer the question. Below is the scatterplot showing the association between raw material (in tons) put into an injection molding machine each day (x), and the amount of scrap plastic (in tons) that is collected from the machine every 4 weeks (y). The residual plot of the data is also shown along with a QQ plot of the residuals. -Choose the statement that best describes whether the condition for normality of errors does or does not hold for the linear regression model.

The regression output below is the result of testing whether there is an association between the number of practice test problems a student completed and the number of questions answered correctly on the test. Assume that the conditions of the linear regression model are satisfied. What is the 95% confidence interval for the slope (rounded to the nearest hundredth)? Does this interval support the theory that the slope is zero? Write a statement that summarizes your answer in context. Coefficients Standard Error Lower 95\% Upper 95\% Intercept -2.12319885 2.3432 -8.14673883 3.90034114 Slope 1.108789625 0.0977 0.85765303 1.359926221

Suppose that you were presented with data showing the association between days absent from class and final class average. Which of the following residual plots below suggests that the Association between number of days absent from class and final class average is linear?