AP Stats Chapter 3

Which statements below about least-squares regression are correct?

• Only I is correct.

• Only II is correct.

• Only III is correct.

• Both II and III are correct.

• All three statements—I, II, and III—are correct.

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?

• 85.5

• 90

• 9

• 95.5

• none of these

In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was yˆ =10+0.9x where y is the final-exam score and x is the score on the first test. Bill scored a 90 on the first test and a 93 on the final exam. What is the value of his residual?

• –2.0

• 2.0

• 3.0

• 93

• none of these

A set of data describes the relationship between the size of annual salary raises and the performance ratings for employees of a certain company. The least squares regression equation is y-hat= 1400 + 2000x where y is the raise amount (in dollars) and x is the performance rating. Which of the following statements must be true?

• For each one-point increase in performance rating, the raise will increase on average by $1400.

• The actual relationship between salary raises and performance rating is linear.

• The residuals for half the observations in the dataset will be positive.

• The correlation between salary raise and performance rating is negative.

• If the mean performance rating is 1.2, then the mean raise is $3800.

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Is this a probability distribution?

• No

• Yes

• A

• B

• C

• D

• E

A least-squares regression line for predicting weights of basketball players on the basis of their heights produced the residual plot below. What does the residual plot tell you about the linear model?

• A residual plot is not an appropriate means for evaluating a linear model.

• The curved pattern in the residual plot suggests that there is no association between the weight and height of basketball players.

• The curved pattern in the residual plot suggests that the linear model is not appropriate.

• There are not enough data points to draw any conclusions from the residual plot.

• The linear model is appropriate, because there are approximately the same number of points above and below the horizontal line in the residual plot.

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that

• minimizes the sum of the distances between the actual UV values and the predicted UV values.

• minimizes the sum of the squared residuals between the actual yield and the predicted yield.

• minimizes the sum of the distances between the actual yield and the predicted UV.

• minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values.

• minimizes the perpendicular distance between the regression line and each data point.

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: Which of the following is correct?

• If the UV value increases by 1 Dobson unit, the yield is expected to increase by 0.0463 kg.

• If the yield increases by 1 kg, the UV value is expected to decrease by 0.0463 Dobson units.

• If the UV value increases by 1 Dobson unit, the yield is expected to decrease by 0.0463 kg.

• The predicted yield is 4.3 kg when the UV value is 20 Dobson units.

• None of the above is correct.