A student performs a linear regression on a dataset and finds the correlation coefficient is $r = 0.98$. What does this value signify?

The data has a strong positive linear relationship.

The data has a strong negative linear relationship.

The data has a weak or no linear relationship.

The slope of the line of best fit is 0.98.

What is the primary purpose of using the LinReg function on a graphing calculator with two lists of data?

To find the equation for the line of best fit.

To calculate the average of the data points.

To solve a system of linear equations.

To create a scatter plot of the data.

A linear regression analysis on study hours ($x$) and test scores ($y$) yields the equation $y = 5.5x + 42$. How should the slope, 5.5, be interpreted?

For each additional hour of study, the test score is predicted to increase by 5.5 points.

The lowest predicted test score is 5.5.

The average test score for all students is 5.5.

A student who studies for 0 hours is predicted to score 5.5.

Analyzing Lines of Fit Practice — Grade 8 math

Lesson 5: Analyzing Lines of Fit — Practice Questions

1. A student performs a linear regression on a dataset and finds the correlation coefficient is $r = 0.98$. What does this value signify?
- A. The data has a strong positive linear relationship.
- B. The data has a strong negative linear relationship.
- C. The data has a weak or no linear relationship.
- D. The slope of the line of best fit is 0.98.
2. Using a calculator for the data points (2, 8), (4, 13), (6, 19), and (8, 24), the line of best fit is found to be $y = ax + b$. What is the value of the slope, $a$, rounded to one decimal place? ___
3. A linear regression is performed on the data set {(5, 20), (10, 31), (15, 42), (20, 54)}. The resulting equation is $y = 2.26x + b$. What is the value of the y-intercept, $b$, rounded to one decimal place? ___
4. What is the primary purpose of using the LinReg function on a graphing calculator with two lists of data?
- A. To find the equation for the line of best fit.
- B. To calculate the average of the data points.
- C. To solve a system of linear equations.
- D. To create a scatter plot of the data.
5. A linear regression analysis on study hours ($x$) and test scores ($y$) yields the equation $y = 5.5x + 42$. How should the slope, 5.5, be interpreted?
- A. For each additional hour of study, the test score is predicted to increase by 5.5 points.
- B. The lowest predicted test score is 5.5.
- C. The average test score for all students is 5.5.
- D. A student who studies for 0 hours is predicted to score 5.5.
6. For a data point $(4, 15)$ and a line of fit given by the equation $y = 3x + 5$, what is the residual? ___
7. If the residual for a data point is positive, what does this indicate about the actual data point's position relative to the line of fit?
- A. The point lies below the line of fit.
- B. The point lies on the line of fit.
- C. The point lies above the line of fit.
- D. The line of fit is not a good model.
8. A line of fit is modeled by $y = -2x + 10$. For the observed data point $(3, 3)$, calculate the residual. ___
9. A researcher examines a residual plot and notices the points are randomly scattered around the horizontal axis (y=0) with no obvious pattern. What can be concluded?
- A. A linear model is likely a good fit for the data.
- B. A linear model is not appropriate for the data.
- C. The original data has a negative correlation.
- D. All the residuals are positive.
10. An actual data point is $(10, 22)$. The line of fit predicts a value of $y = 25$ for $x=10$. What is the residual for this data point? ___