AP Stats Chapter 3 Review

An agricultural economist says that the correlation between corn prices and soybean prices is r = 0.7. This means that

• when corn prices are above average, soybean prices also tend to be above average.

• there is almost no relation between corn prices and soybean prices.

• when corn prices are above average, soybean prices tend to be below average.

• when soybean prices go up by 1 dollar, corn prices go up by 70 cents.

• the economist is confused, because correlation makes no sense in this situation.

If bivariate data set A has correlation r = 0.95, and a second bivariate data set B has correlation r = –0.95, then

• a linear model does a better job of describing the relationship between the variables in data set A than in data set B.

• a linear model does a better job of describing the relationship between the variables in data set B than in data set A.

• a linear model is the best description of the relationship between the variables in both data set A and data set B.

• you can’t tell whether either data set is best described by a linear model until you examine the scatterplots.

• a mistake has been made—r cannot be negative.

A copy machine dealer has data on the number of copy machines x at each of 89 customer locations and the number of service calls in a month y at each location. Summary calculations give x̅= 8.4, sx= 2.1, y̅= 14.2, sy= 3.8, and r = 0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers?

• 0.86

• 1.56

• 0.48

• 2.82

• cannot tell from the information given

Suppose we fit a least-squares regression line to a set of data. What is true if a plot of the residuals shows a curved pattern?

• a straight line is not a good model for the data

• the correlation must be 0

• the correlation must be positive

• outliers must be present

• The regression line might or might not be a good model for the data, depending on the extent of the curve.

The table shown is comparing a person's foot length to their height in cm. Calculate the regression equation

• yhat = 25.05x + 5.57

• yhat = 5.57x + 25.05

• yhat = -5.57x + 25.05

• yhat = 5.57x - 25.05

The point in the upper right hand corner of the scatterplot is

• not an outlier or an influential point

• not an outlier but an influential point

• an outlier and an influential point

• an outlier but not an influential point

Write the linear regression equation for the data set foot length (x) and height (y).

• yhat = 28.93 + 1.155x

• height = 28.39(foot length) + 1.155

• yhat = 1.878 + 117.99x

• height = 117.99 + 1.878(foot length)

What is the correlation value?

• .209

• .457

• .13

• .361

The following scatterplot describes the relationship between height (in cm) and foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. Which of the following is the best description of this relationship?

• There is some random variation, but otherwise height is directly proportional to foot length.

• There is a roughly linear relationship between height and foot length.

• There is a moderately weak, positive linear relationship between height and foot length.

• The relationship between height and foot length is linear, positive, and very strong.

One of the following is a correct statement involving correlation. The other three contain blunders. Which one is correct? 

• The correlation between the gas mileage of a car and its weight is r = -0.71 gallon-pounds.

• The correlation between GPA and hours of sleep per night is r = 1.06.

• There is a correlation of r = 0.54 between the position a football player plays and his or her weight.

• The correlation between amount of fertilizer and pounds of tomatoes harvested was found to be r = 0.33.