Exam 3: Describing Bivariate Data

When the price of gasoline gets high, consumers become very concerned about the gas mileage obtained by their cars. One consumer was interested in the relationship between car engine size (number of cylinders) and gas mileage (miles/gallon). The consumer took a random sample of 7 cars and recorded the following information: and Would you expect the correlation between engine size and gas mileage to be positive or negative? ______________ Find the correlation between engine size and gas mileage. ______________ Find the best fitting line relating car engine size and gas mileage. y = ______________ What would you predict the gas mileage to be for a car with 6-cylinder engine size? ______________ mpg

If the correlation coefficient , then all the data points lie exactly on a straight line.

Male and female respondents to a questionnaire about gender differences are categorized into three groups according to their answers as shown below: Create a side-by-side bar chart to describe these data. Create two pie charts (one for men and one for women) to describe these data. Men: Women: Which of the charts created above best depicts the difference or similarity of the responses of men and women. ______________

The standard deviation is a measure of the linear relationship between two quantitative variables.

A perfect straight line sloping upward would produce a covariance value of +1.

Which of the following are measures of the linear relationship between two variables?

A manager of a supermarket wishes to show the relationship between the number of customers who come to the store on weekends, and the total volume of sales (in dollars) during the same weekend. Which of the following graphs would likely be most useful if the manager has a sample of 52 weekends worth of data?

If the correlation coefficient , then there is no linear relationship whatsoever between the dependent variable y and the independent variable x.

A perfect straight line sloping downward would produce a correlation coefficient equal to:

A councilman was interested in determining whether people between the ages of 18 and 30 years of age will react to a piece of legislation differently than people over 30 years of age. The legislator polled a sample of 150 people from his district. The resulting data is shown in the table below: Construct a side-by-side bar chart. Construct a pie chart for the 18 - 30 age group. Construct a pie chart for the Over 30 age group. Which of the two types of presentations in parts (a) and (b) is more easily understood? ______________

If all the points in a scatterplot lie on the least squares regression line, then the correlation coefficient r must be:

A soft drink distributor was interested in examining the relationship between the number of ads (x) for his product during prime time on a local television station and the number of sales per week (y) in thousands of cases. He compiled the figures for 20 weeks and computed the following summary information: and Find the correlation coefficient for the number of ads during prime time and weekly sales. ______________ Find the best-fitting line relating the number of ads during prime time and weekly sales. y = ______________ If the soft drink distributor ran 21 TV ads per week for his product, what would you predict his sales to be? ______________ thousand cases

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

Given that = 100, = 64, = 60, and n = 8, the slope of the best-fitting regression line is:

A scatterplot is not particularly useful in determining if the relationship between the independent and dependent variables is not linear.

A perfect straight line sloping downward would produce a covariance value of -1.

Which value of the correlation coefficient r indicates a stronger correlation than 0.72?

The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activities. The following output was generated using Minitab: Covariances Let x = weekly take-home pay, and y = amount spent weekly on recreational activities. a. Identify the covariance between x and y. ______________ b. Identify the variance of weekly take-home pay. ______________ c. Identify the variance of amount spent weekly on recreational activities. ______________ d. Calculate the correlation between weekly take-home pay and amount spent weekly on recreational activities. ______________ e. Interpret the correlation coefficient found in part (d). ____________________________

If the linear relationship between the dependent and independent variables is positive, the scatterplot will show the data points on the (x, y) plane generally moving from the lower left corner to the upper right corner.

When constructing a scatterplot, the independent variable (x) is placed on the horizontal axis, and the dependent variable (y) is placed on the vertical axis.