AP Statistics - Module 6 MCQ Review - Days 1 - 4

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river.

Which of the following statements is a correct interpretation of the value 19.0 in the output?

• On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.

• On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.

•  The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.

• The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.

• Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.

There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model

ŷ = 25.2 + 3.3x, where x is the number of chirps per minute and ŷ is the estimated temperature in degrees Fahrenheit.

What is the predicted increase in temperature that corresponds to an increase of 5 chirps per minute?

•  3.3° F

•  16.5° F

•  25.2° F

•  28.5° F

•  41.7° F

Exercise physiologists are investigating the relationship between lean body mass (in kilograms) and the resting metabolic rate (in calories per day) in sedentary males.

Based on the computer output above, which of the following is the best interpretation of the value of the slope of the regression line?

• For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 22.563 calories per day.

• For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 264.0 calories per day.

• For each additional kilogram of lean body mass, the resting metabolic rate increases on average by 144.9 calories per day.

• For each additional calorie per day for the resting metabolic rate, the lean body mass increases on average by 22.563 kilograms.

• For each additional calorie per day for the resting metabolic rate, the lean body mass increases on average by 264.0 kilograms.

Consider n pairs of numbers (x₁,y₁), (x₂,y₂), ..., and (x_n, y_n). The mean and standard deviation of the x-values are x̄ =5 and s_x = 4, respectively. The mean and standard deviation of the y-values are ȳ = 10 and s_y = 10 respectively. Of the following, which could be the least squares regression line?

• ŷ = -5.0 + 3.0x

• ŷ = 3.0x

• ŷ = 5.0 + 2.5x

• ŷ = 8.5 + 0.3x

• ŷ = 10.0 + 0.4x

The correlation coefficient measures

•  Whether there is a relationship between two variables

• The strength of the relationship between two quantitative variables

• Whether or not a scatterplot shows an interesting pattern

• Whether a cause and effect relation exists between two variables

• The strength of the linear relationship between two quantitative variables

  
  

Which of the following is true of the correlation r?

• It is a resistant measure of association

•  −1 ≤ r ≤ 1

•  If r is the correlation between X and Y, then –r is the correlation between Y and X

• Whenever all the data lie on a perfectly straight-line, the correlations r will always be equal to +1.0

• All of the above

A study gathers data on the outside temperature during the winter in degrees Fahrenheit and the amount of natural gas a household consumes in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least squares regression line for predicting y from x is ŷ = 1344 - 19x.

When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line?

•  It goes up 19 cubic feet

• It goes down 19 cubic feet

•  It goes up 1344 cubic feet

• It goes down 1344 cubic feet

• Can’t tell without seeing the data

A least squares regression line is created for predicting stopping distance (y) in feet from temperature (x) in degree Fahrenheit. If stopping distance was expressed in yards instead of feet, how would the correlation r between temperatures and stopping distance change?

• r would be divided by 12

•  r would be divided by 3

• r would not change

• r would be multiplied by 3

• r would be multiplied by 12

The percent of variation in the values of y that is explained by the least-squares regression of y on x is

• the correlation coefficient.

• the slope of the least-squares regression line.

• the square of the correlation coefficient.

• the intercept of the least-squares regression line.

• the slope of the transformed exponential function.

Which of the following statements about influential points are true?

I. Influential points have large residuals

II. Removal of an influential point sharply affects the regression line

III. Outliers are always influential points

• I and II

• I and III

•  II and III

• I, II, and III

• None of the above gives the complete set of true responses.