Exam 4: Regression Analysis: Exploring Associations Between Variables

Doctors believe that smoking cigarettes inflames the bronchial tubes and so makes it harder to Doctors believe that smoking cigarettes inflames the bronchial tubes and so makes it harder tobreathe. To test this they measured the lung capacity (in liters) and the number of cigarettessmoked in a typical day for a sample of adults. Is the scatterplot below consistent with theresearcher's hypothesis?

Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot below.

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park. $\text { Ticket sales per hour } = - 631.25 + 11.25 \text { (current temperature in } { } ^ { \circ } \mathrm { F } \text { ) }$ -Choose the statement that best states the meaning of the slope in this context.

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.3120$

City Size (in thousands) Grocery Expenditures (in hundreds of dollars) 30 65 50 77 75 79 100 80 150 82 200 90 175 84 120 81 -Based on the scatterplot, estimate the correlation coefficient between city size andexpenditures for these eight families. Explain your reasons for choosing your estimate.

Use the following information to answer the question. A scatterplot of data from a large sample of adult women shows thatheight in inches and weight in pounds have a linear association. Shown below are the outputs from two different statisticaltechnologies (TI-83/84 Calculator and Excel). T-Test y=a+bx a=-23.86734694 b=2.581632653 =.7648162309 r=.8745377241 Coefficients Intercept -23.86734694 X Variable 1 2.581632653 -Height and weight charts for women show that a woman who is 71 inches tall has a targetweight between 135 and 176 pounds. Would the regression model you found for the largesample of (in question 15) place a woman who was 71 inches tall within this range?

The scatterplot below shows the number of tackles received and the number of concussions received for a team of football players for the most recent season. Choose the statement that best describes the trend.

Choose the scatterplot that matches the given correlation coefficient. - $r = 0.8670$

Explain in your own words what extrapolation is and give an example. Why shouldextrapolation be avoided when doing regression analysis?

Use the regression equation to predict how many children a married couple will have ifthey live in city with a population of 40,000 people.

Suppose it has been established that "home value" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Home value $= \$ 75,000 + \$ 12,500$ (Years of College). In this model, "years of college" is the $\frac{?}{}$ variable, and "home value" is thehave a $\frac{?}{}$ variable. The two variables have a $\frac{?}{}$

If the correlation between whole milk content per serving and calories per serving forseveral brands of ice cream is 0.71, report the coefficient of determination (rounded to thenearest tenth of a percent) and explain what it means using a complete sentence. Assumethat whole milk content is the predictor and calories per serving is the response, andassume that the association between whole milk content and calories is linear.

In the NHL, the correlation between "Goals scored per game" and "minutes on the ice" for a team of players is found to be 0.8178. Choose the statement that is true about the coefficient of determination.

Use the following information to answer the question. The following linear regression model can be used to predict ticketsales at a popular water park. Ticket sales per hour=-631.25+11.25(current temperature in °F) -What is the predicted number of tickets sold per hour if the temperature is 86°F? Round to the nearest whole ticket.

A horticulturist conducted an experiment on 120 thirty-six inch flower boxes to see if theamount of plant food given to the flower boxes was associated with the number of bloomson the plants. The average amount of plant food given was 31.6 milliliters with a standarddeviation of 2.2 milliliters. The average number of blooms was 10.5 with a standarddeviation of 1.5. The correlation coefficient was 0.8891. Use the information to calculate theslope of the linear model that predicts the number of blooms from the amount of plantfood given. Show your work and round to the nearest hundredth. Write a sentenceexplaining the meaning of the slope in this context.

Suppose that in the Midwest, it is shown that there is trend between home insuranceclaims in dollars and the number of cattle owned by the home owner. The trend shows thathigher claims were paid out to homeowners that owned more cattle. Does this trend provethat owning more cattle causes higher insurance claims? Be sure to explain your reasoning,don't just answer yes or no. What is a potential hidden variable in this context?

Choose the scatterplot that matches the given correlation coefficient. - $r = - 0.6542$

Use the following information to answer the question. The following linear regression model can be used to predict ticketsales at a popular water park. Ticket sales per hour $= - 631.25 + 11.25 \left( \right.$ current temperature in ${ } ^ { \circ } \mathrm { F }$ ) -In this context, does the intercept have a reasonable interpretation?

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expendituresfor eight families. City size is in thousands and expenditures is in hundreds of dollars. City Size (in thousands) Grocery Expenditures (in hundreds of dollars) 30 65 50 77 75 79 100 80 150 82 200 90 175 84 120 81 -State the explanatory variable and the response variable.

The following model was created to show the association between the number of massagesreceived per month and self-predicted stress level: Stress level=10-0.02(number of massages permonth). The coefficient of determination for the model is 0.066 or 6.6%. Choose the true statementregarding this model.