Exam 4: Regression Analysis: Exploring Associations Between Variables

Suppose it has been established that "annual income" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Annual Income = $23,400+$7200(Years of College). In this model, "Annual Income" is the ? variable, and "Years of College" is the ? variable. The two variables have a ? linear relationship.

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 statement that best states the meaning of the slope in this context.

r = 0.8670

The following regression equation was found to model commute distance (in miles)and number of minor accidents per year for a group of adults. Minor accidents per year = 1.204 + 0.024(commute distance) What is the intercept? What is the interpretation of the intercept in this context? Does it make sense to interpret the intercept in this context?

Suppose that environmentalists monitor algae levels in a river and determine that there is a linear association between local rainfall and algae levels. The determine that the best fitting linear model to predict algae cell counts per milliliter from rainfall in inches is: Algae cell count = 229.32 + 79.81(Rainfall in inches)with r² = 0.604 How will a rainfall that is 3 inches above average affect the algae cell count?

The following calculator screenshots show the scatterplot and the correlation coefficient between the number of days absent and the final grade for a sample of college students in a general education statistics course at a large community college. The relationship between "days absent" and "final grade" can be described as

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) -In this context, does the intercept have a reasonable interpretation?

A horticulturist conducted an experiment on 110 thirty- six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of tomatoes harvested from the plants. The average amount of plant food given was 27.8 milliliters with a standard deviation of 2.1 milliliters. The average number of tomatoes harvested was 7.5 with a standard deviation of 1.5. The correlation coefficient was 0.7691. Use the information to calculate the slope of the linear model that predicts the number of tomatoes harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

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) -Choose the statement that best states the meaning of the slope in this context.

Suppose that in the Midwest, it is shown that there is trend between home insurance claims in dollars and the number of cattle owned by the home owner. The trend shows that higher claims were paid out to homeowners that owned more cattle. Does this trend prove that 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?

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. -Using the data from the table, sketch a scatterplot (by hand or with the aid of technology)of the data. Describe any association that you see. Would it be appropriate to fit a linear model to this data?

A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is and the response variable is .

Doctors hypothesize 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?

The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below.

The following regression equation was found to model commute distance (in miles)and number of minor accidents per year for a group of adults. Minor accidents per year = 1.204 + 0.024(commute distance)Identify the independent variable and the dependent variable.

It is determined that a positive linear association exists between age (for children between the ages of 3 and 9 years)and attention span (measured in minutes). The scatterplot below shows the association. The prediction equation is also given. A college instructor uses the model to predict the attention span of the students in her class who have an average age of 29. Choose the best statement to summarize why this is not an appropriate use for the model. attention span = 4.68 + 3.40(age)

A horticulturist conducted an experiment on 140 thirty- six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of habanera peppers harvested from the plants. The average amount of plant food given was 17.8 milliliters with a standard deviation of 0.7 milliliters. The average number of habanera peppers harvested was 6.5 with a standard deviation of 1.5. The correlation coefficient was 0.8123. Use the information to calculate the slope of the linear model that predicts the number of habanera peppers harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

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) -In this context, does the intercept have a reasonable interpretation?

It is determined that a positive linear association exists between amount of a new smoking cessation drug taken (in milliliters)and weight gain in women (in pounds). The scatterplot below shows the association. The prediction equation is also given. A pharmacy technician uses the model to predict the potential weight gain for a man who takes the recommended dosage. Choose the best statement to summarize why this is not an appropriate use for the model.