Exam 4: Regression Analysis: Exploring Associations Between Variables

Use the following information for following questions:. The scatterplot below shows the relationship between the ages of women when they first married and the ages when they had their first child. The correlation coefficient between the values is -Can we use the regression equation to predict the age at which a woman has her first child for a woman who first married at the age of 50?

Use the following regression equation regarding car mileage for following questions . Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways. -Interpret the slope in the context of the data.

Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables?

Use the following regression equation regarding car mileage for following questions . Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways. -Interpret the intercept in the context of the data. State whether the value is meaningful.

Use the following information for following questions . Data were recorded for 117 months on a household's gas bill (in dollars) and the average monthly temperatures for its neighborhood. The mean monthly temperature was 48.7° F with a standard deviation of 20.6. The mean gas bill price was $81.20 with a standard deviation of 66.5. The correlation coefficient between monthly temperature and gas bill price is −0.92. -Determine the correct value of the slope for the linear model that predicts gas bill price from monthly temperature and interpret it in context.

Use the following information for following questions . Suppose data were recorded for 100 employees of a large company that included annual salaries and the number of years the employee has been in their current position. The mean annual salary was $58,000 with a standard deviation of 12,500. The mean number of years in the current position is 10 with a standard deviation of 3. The correlation coefficient between the two variables is approximately 0.93. -Calculation the value of the intercept for the linear model that predicts annual salary from the number of years in current position and interpret it in context, if appropriate.

Use the following information for following questions . A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg was 35 with a standard deviation of 8.6. The correlation coefficient between city mpg and highway mpg is -Determine which is the correct calculation of the intercept for the linear model that predicts highway mpg from city mpg.

Which of the following sets of numbers would result in a negative correlation of −1?

For any set of data, the regression equation will always pass through

Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables?

Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables? Explain your reasoning.

Suppose daily high and low temperature measures were taken for 50 days. For each day, the daily high temperature was exactly 10 degrees higher than the daily low temperature. For example, on a day with a high temperature of 80° , the low temperature was 70° . What is the best estimate of the correlation coefficient between the daily high and daily low temperatures?

Suppose 50 married couples are asked to provide their ages. For all couples, the husband is exactly 2 years older than his wife. For example, a 50- year-old husband has a wife who is 48 years old. What is the best estimate of the correlation coefficient between the ages of husbands and their wives?

Which of the following statements regarding the correlation coefficient is false?

Use the following information to answer Questions . The scatterplot below shows the relationship between the average monthly temperature and the monthly cost of a gas bill. The correlation coefficient between the values is −0.92. -Determine the value of the coefficient of determination and explain its meaning in context?

Use the following information to answer Questions . The scatterplot below shows the relationship between a car's speed and the distance it traveled to come to a complete stop when hitting the brakes. The correlation coefficient between the values is 0.81. -Would it be appropriate to say that a car's speed causes its stopping distance?

Use the following regression equation regarding professor salaries for following questions . ) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns. -What is the expected salary of a professor who has worked at a college for 15 years?

Use the following information to answer Questions . The scatterplot below shows the relationship between a car's speed and the distance it traveled to come to a complete stop when hitting the brakes. The correlation coefficient between the values is 0.81. -Can we use the regression equation to predict the stopping distance of a car that is traveling at 40 mph?

Use the following information to answer Questions . The scatterplot below shows the relationship between a car's speed and the distance it traveled to come to a complete stop when hitting the brakes. The correlation coefficient between the values is 0.81. -[Objective: Interpret the coefficient of determination in context.] What is the value of the coefficient of determination and what does it mean in context?

Use the following regression equation regarding airline tickets for following questions . Note that Distance is the amount of miles between the departure and arrival cities, and Price is the cost of an airline ticket. -Interpret the intercept of the regression equation in the context of the data. Explain why the value is or is not meaningful.