Home / AP® Exam / AP® Statistics / 2.8 Least Squares 2 Regression- MCQs

AP Statistics 2.8 Least Squares 2 Regression- MCQs - Exam Style Questions

AP Statistics -MCQs and Answers - All Topics

Question

The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was \(0.8\). Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
(A) On average, the height of a child is \(80\%\) of the age of the child.
(B) The least-squares regression line of height versus age will have a slope of \(0.8\).
(C) The proportion of the variation in height that is explained by a regression on age is \(0.64\).
(D) The least-squares regression line will correctly predict height based on age \(80\%\) of the time.
(E) The least-squares regression line will correctly predict height based on age \(64\%\) of the time.
▶️ Answer/Explanation
Detailed solution

The correlation coefficient is \(r=0.8\). The coefficient of determination is \(r^2\), which gives the proportion of variation in the response (height) explained by the linear regression on the explanatory variable (age).
Compute \(r^2=(0.8)^2=0.64\). Thus, about \(64\%\) of the variation in height is explained by the regression on age.
Statements about the slope or prediction “percent correct” misinterpret \(r\).
✅ Answer: (C)

Question

A consumer group wanted to investigate the relationship between the number of items purchased at a single visit to the local grocery store and the total cost of the items purchased. The group obtained a random sample of 11 receipts from the store and recorded the total number of items and the total cost from each receipt. The computer output of an analysis of total cost versus number of items purchased is shown in the table.
 EstimateStd Errort RatioProb>|t|
Intercept1.8826.68540.280.7847
Number of items2.7840.226512.29<0.0001
Assume all conditions for inference were met. Based on the results shown in the table, which of the following is a 95 percent confidence interval for the average change in total cost for each increase of 1 item purchased?
(A) $2.784\pm12.29(0.2265)$
(B) $2.784\pm2.262(0.2265)$
(C) $2.784\pm2.262(\frac{0.2265}{\sqrt{11}})$
(D) $1.882\pm1.96(6.6854)$
(E) $1.882\pm2.262(6.6854)$
▶️ Answer/Explanation
Detailed solution

1. Identify the Goal and Formula:
We need a 95% confidence interval for the slope of the regression line. The slope represents the average change in cost for each additional item.
The general formula is: $b \pm t^*(SE_b)$

2. Extract Values from the Table:
– The slope estimate ($b$) is the coefficient for “Number of items”: $b = 2.784$.
– The standard error of the slope ($SE_b$) is given in the same row: $SE_b = 0.2265$.

3. Determine the Critical Value ($t^*$):
– The confidence level is 95%.
– The degrees of freedom ($df$) for slope in linear regression is $n-2$.
– With a sample size of $n=11$, we have $df = 11 – 2 = 9$.
– The critical value $t^*$ for 95% confidence with 9 degrees of freedom is 2.262.

4. Construct the Interval:
Substitute the values into the formula:
$2.784 \pm 2.262(0.2265)$
✅ Answer: (B)

More AP Statistics MCQ Questions..
Scroll to Top