AP Statistics Two Variable Data Review

Measurements on young children in Mumbai, India, found this least-squares line for predicting height (cm) y from arm span (cm) x: y-hat = 6.4 + 0.93x According to the regression line, the predicted height of a child with an arm span of 100 cm is about

• 106.4 cm

• 99.4 cm

• 93 cm

• 15.7 cm

• 7.33 cm

Does the residual plot support the appropriateness of a linear model?

• Yes because the residual plot has no apparent pattern

• Yes because half the residuals are positive and half are negative

• No because points appear to be randomly distributed

• No because some points are close to the line when others are not

• Yes, because as age increases, the residuals increase

What can you know from the relative frequency graph?

• The same amount of people were in each continent in 2011 (orange)

• More people were in Asia in 2012

• More people were in North America overall

• More people were in North America in 2010

• A greater percentage of people were in North America than the other continents in 2010

Describe the mean and median of this distribution.

• Due to the skew, the mean is greater than the median

• Due to the skew, the median is greater than the mean

• The median is equal to the mean

• The mean cannot be estimated from the histogram, but the median can

• The median cannot be estimated from the histogram, but the mean can

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.

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.

The correlation (r) between high school students' height (in inches) and weight (in pounds) for a large sample of students is found to be 0.3. If the weight measurements are converted to kg, what will be the resulting correlation?

• 0.3

• 0.66

• -0.3

• 0.136

Data is obtained for a large group of college students relating the time they spent writing an essay and the grade on the essay. The equation is grade = 30.18 + 6.49(time) with r = 0.724 What percentage of the variation in grades can be explained by looking at time spent on the essay?

• 52.4%

• 72.4%

• 27.6%

• 47.6%