If the residual for a data point is negative, what does this imply about the point's position relative to the line of best fit?

The point is located directly on the line of best fit.

The point is located above the line of best fit.

The point is located below the line of best fit.

A statistician creates a residual plot and observes that the points form a distinct U-shaped curve. What is the most appropriate conclusion?

A linear model is a good fit for the data.

A linear model is not a good fit for the data.

The calculation of residuals must be incorrect.

Which of the following descriptions of a residual plot indicates that a linear model is an appropriate fit for the data?

The residuals form a clear, increasing line.

The residuals are all positive.

The residuals are randomly scattered around the x-axis.

The residuals form a funnel shape.

Analyzing Lines of Fit Practice — Grade 11 math

Lesson 6: Analyzing Lines of Fit — Practice Questions

1. A line of best fit predicts a value of $y = 21.5$ when $x = 10$. If the actual data point is $(10, 25)$, what is the residual? The residual is ___.
2. For a data point $(4, 15)$, a linear model predicts a value of $y = 18.8$. Calculate the residual for this data point. The residual is ___.
3. If the residual for a data point is negative, what does this imply about the point's position relative to the line of best fit?
- A. The point is located directly on the line of best fit.
- B. The point is located above the line of best fit.
- C. The point is located below the line of best fit.
- D. The point is an outlier.
4. A statistician creates a residual plot and observes that the points form a distinct U-shaped curve. What is the most appropriate conclusion?
- A. A linear model is a good fit for the data.
- B. A linear model is not a good fit for the data.
- C. The calculation of residuals must be incorrect.
- D. The data has no correlation.
5. Which of the following descriptions of a residual plot indicates that a linear model is an appropriate fit for the data?
- A. The residuals form a clear, increasing line.
- B. The residuals are all positive.
- C. The residuals are randomly scattered around the x-axis.
- D. The residuals form a funnel shape.
6. What is the primary purpose of drawing a line of best fit on a scatter plot?
- A. To connect every data point in the plot.
- B. To show the overall trend or pattern in the data.
- C. To calculate the average of the x-values and y-values.
- D. To identify the exact minimum and maximum values.
7. A line of best fit is a straight line that models the relationship between two variables. It is also known as a(n) ___ line.
8. A scatter plot relates the number of hours a student plays video games and their test scores. If the line of best fit has a negative slope, what does this suggest?
- A. More gaming is associated with higher scores.
- B. More gaming is associated with lower scores.
- C. Gaming has no effect on scores.
- D. The data is incorrect.
9. Which of the following statements about a line of best fit is always true?
- A. It must pass through at least half of the data points.
- B. It must be expressed in the form $y = mx + b$.
- C. It must pass through the origin $(0,0)$.
- D. It must connect the first and last data points.
10. A line of best fit is drawn for a set of data points. It is possible for the line to pass through ___ of the points.