Exam 4: Regression Analysis: Exploring Associations Between Variables

Use the following information for following questions . The scatterplot shows the relationship between the foot lengths and foot widths of children. The coefficient of determination was found to be 41.09%. -Calculate the value of the correlation coefficient between a car's age and its current value.

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. -If appropriate, calculate the expected gas bill cost for a month with an average temperature of − . If it's not appropriate, explain why.

Use the following information for following questions . The following scatterplot shows the relationship between heights (in cm) and weights (in kg) of 100 Americans. The coefficient of determination was found to be 37.9%. -If we converted the x- axis to inches, instead of centimeters, what would happen to the value of the correlation coefficient?

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 which is the correct calculation of the intercept for the linear model that predicts gas bill price from monthly temperature.

Which scatterplot below depicts a stronger linear relationship? Why?

Given the following scatterplot, if a point was added in the upper left corner with an x-value of 10 and a y-value of 20, what would happen to the value of the correlation coefficient, r?

[Objective: Determine the effects of outliers on a regression equation.] What effects might an outlier have on a regression equation?

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. -Interpret the slope in the context of the data.

Use the following information for following questions The scatterplot shows the relationship between a vehicle's age (in years) and its current value (in dollars). The coefficient of determination was found to be 98.74%. -Calculate the value of the correlation coefficient between a car's age and its current value.

A study about high school student SAT scores reported that a student's SAT Math score has a strong positive linear association with his/her SAT Verbal score. What can you determine about the relationship between SAT Math scores and SAT Verbal scores?

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 -Would it be appropriate to say that the age at which a woman first marries causes her to have her first child after that age?

Suppose the heights of teenagers were recorded in 2003 and then recorded again 5 years later, in 2008. For each person, the height in 2008 was 6 inches (15.24 centimeters) taller than the height in 2003. For example, a teenager who was 53 inches (134.62 cm) tall in 2003 measured at a height of 59 inches (149.86 cm) in 2008. What would be the correlation coefficient between the 2003 heights and the 2008 heights? Explain your reasoning.

Use the following information for following questions . The scatterplot shows the relationship between the foot lengths and foot widths of children. The coefficient of determination was found to be 41.09%. -If we converted the x-axis to inches, instead of centimeters, what would happen to the value of the correlation coefficient?

Given the following scatterplot, if the point in the upper left corner were removed, what would happen to the value of the correlation coefficient, r?

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. -What is the expected highway mpg for a car that gets 23 mpg in cities?

Use the following information for following questions The scatterplot shows the relationship between a vehicle's age (in years) and its current value (in dollars). The coefficient of determination was found to be 98.74%. -If we converted the x-axis to months, instead of years, what would happen to the value of the correlation coefficient?

When will a correlation coefficient be negative?

Suppose the ages and heights of 100 randomly selected people were recorded. Which variable is the explanatory variable and which one is the response?

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. -What is the expected ticket price for a flight between Los Angeles and New York City, which are 2448.3 miles apart?

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. -If an employee earns an annual salary of $85,000, approximately how long has she held her current position at the company? Round your answer to the nearest year.