Exam 4: Regression Analysis: Exploring Associations Between Variables

What key things should you look for when examining the potential linear association between two variables?

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. 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 79°F? Round to the nearest whole ticket.

r = - 0.3526

The scatterplot below shows the number of alcoholic drinks consumed and memory test results for some college students. Is there an association? If so, describe the pattern. Be sure to comment on trend, shape, and the strength of the association.

The scatterplot below shows the ice cream sales and daily high temperatures for a three week period of time during the summer. Does there appear to be an association between these two variables? If so, describe the pattern. Be sure to comment on trend, shape, and the strength of the association.

The figures below show the relationship between salary and personal lunch expenses on week days for a group of business men. Comment on the difference in graphs and in the coefficient of determination between the graph that includes a data point of someone who reported earnings of $21,000 per year and weekly personal lunch expenses of $100 per week (second graph)and the graph that did not include this data point (first graph).

A concert ticket agent is going to investigate whether an increase in money spent on radio advertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, the response variable is and the explanatory variable is .

r = - 0.6542

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. 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.

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

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars. -Suppose each of these families is given a grocery credit of $100, therefore reducing expenditures in the table by one unit (since this variable was recorded in hundreds of dollars). Estimate the new correlation with city size. What happens to the correlation when a constant is added (in this case - 100 dollars is added to each number)? Explain your reasoning.

The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars. The relationship between "car length" and "car weight" can be described as

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 ? variable, and "home value" is the ? variable. The two variables have a ? .

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. A scatterplot of data from a large sample of adult women shows that height in inches and weight in pounds have a linear association. Shown below are the outputs from two different statistical technologies (TI- 83/84 Calculator and Excel). -Height and weight charts for women show that a woman who is 71 inches tall has a target weight between 135 and 176 pounds. Would the regression model you found for the large sample of (in question 15)place a woman who was 71 inches tall within this range?

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

Use the data provided in the table below to answer the question. The table shows city size and annual grocery expenditures for eight families. City size is in thousands and expenditures is in hundreds of dollars. -Based on the scatterplots below, what is the better predictor for head circumference-- height or shoulder width? Explain how you made your decision.

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. Ticket sales per hour = - 631.25 + 11.25(current temperature in °F) -Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot below.

r = 0.8787

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.