AP Statistics 5.3 Linear Regression Models- Exam Style Questions - MCQs - New Syllabus
▶️ Answer/Explanation
To construct a confidence interval for the true slope, use:
\(\text{Estimate} \pm t^*(SE)\)
The estimated slope is:
\(b_1 = 0.25575\)
The standard error of the slope is:
\(SE_{b_1}=0.0782\)
Since there are \(n=31\) trees, the degrees of freedom are:
\(df=n-2=29\)
For a 95% confidence interval with \(df=29\):
\(t^* \approx 2.045\)
Therefore, the confidence interval is:
\(0.25575 \pm (2.045)(0.0782)\)
✅ Answer: (E)
▶️ Answer/Explanation
The slope of the regression line is -1.1, which means that for every additional year of age, the predicted fleece production decreases by 1.1 ounces per month.
The age difference between the two alpacas is:
\(10-5=5\text{ years}\)
Therefore, the expected difference in fleece production is:
\((-1.1)(5)=-5.5\text{ ounces}\)
This means the 10-year-old alpaca is expected to produce 5.5 fewer ounces per month than the 5-year-old alpaca. Equivalently, the 5-year-old alpaca is expected to produce 5.5 more ounces per month than the 10-year-old alpaca.
✅ Answer: (D)
▶️ Answer/Explanation
A residual is calculated as:
\(\text{Residual}=\text{Observed Value}-\text{Predicted Value}\)
A negative residual means the actual airfare is lower than what the regression line predicts. Therefore, the city with the largest negative residual represents the best airfare value for its distance.
Looking at the scatterplot, City E lies well below the regression line and is farther below the line than any of the other labeled cities. City A and City B are above the line (positive residuals), while Cities C and D are only slightly below it.
Therefore, City E has the largest negative residual and thus the best value in airfare based on distance from Atlanta.
✅ Answer: (E)