Grade 9 Math: Introduction to Regression
Use a line of best fit to make and qualify predictions. Includes a worked example, printable practice, and an answer key with explanations.
The answer key follows the practice below. In the editor, remove the final answer-key section before sharing a student copy.
Use This WorksheetIncludes
Standards
Topics
Introduction to Regression
Name:
Date:
Score:
Learning goal and worked example
Use a line of best fit to make and qualify predictions.
For a fitted line y = 6x + 45, x = 5 predicts 75. The slope means 6 additional score points per extra hour in this model; extrapolating beyond observed hours is less reliable.
Prerequisites: scatter plots, slope, and substitution. Hand-drawn lines may give different reasonable predictions.
Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.
1. Which type of graph is typically used to display the relationship between two quantitative variables?
Bar graph
Histogram
Scatter plot
Pie chart
2. When points on a scatter plot generally rise from left to right, it indicates a correlation.
3. The line that best represents the trend in a scatter plot is called the .
4. Describe what a 'line of best fit' represents in the context of a scatter plot.
5. Consider the following data showing the number of hours studied (X) and the test scores (Y) for 5 students:
Student 1: (2, 60) Student 2: (3, 70) Student 3: (4, 80) Student 4: (5, 85) Student 5: (6, 90)
a) Plot these points on the graph below and draw a line of best fit.
b) Use your line of best fit to predict a score for 7 hours of study. Explain why this is extrapolation and why the prediction is uncertain.
6. A negative correlation means that as one variable increases, the other variable also increases.
True
False
Answer key and worked solutions
1. c (scatter plot). 2. Positive. 3. Line of best fit (or regression line).
4. A line of best fit summarizes the linear trend. A least-squares line minimizes the sum of squared vertical residuals. Not every point must lie on it.
5a. Plot (2,60),(3,70),(4,80),(5,85),(6,90). One precise reference line is the least-squares fit y = 7.5x + 47: x̄=4, ȳ=77, slope=75/10=7.5, intercept=77−7.5×4=47.
5b. This line predicts 7.5×7+47 = 99.5 points. Accept reasonable estimates from a defensible hand-drawn line. Seven hours is outside the observed 2–6-hour range, so this is extrapolation; the trend may not continue and scores are bounded by the test scale.
6. False. In a negative association, one variable tends to decrease as the other increases.
Related Worksheets
Bivariate Data Analysis Worksheet
Read paired quantitative data and explain association without claiming causation. Includes a worked example, printable practice, and an answer key with explanations.
Grade 9 Math: Understanding Variance
Calculate population variance and distinguish it from sample variance. Includes a worked example, printable practice, and an answer key with explanations.
Standard Deviation Worksheet
Calculate population standard deviation and interpret consistency. Includes a worked example, printable practice, and an answer key with explanations.
Grade 9 Chi-Square Test Worksheet
Calculate expected counts and Pearson’s chi-square statistic for a two-way table. Includes a worked example, printable practice, and an answer key with explanations.
Statistical Questions Worksheet
Recognize questions that anticipate variability and summarize responses. Includes a worked example, printable practice, and an answer key with explanations.
Measures of Center Worksheet
Choose and calculate mean, median, and mode. Includes a worked example, printable practice, and an answer key with explanations.
Grade 9 Population Calculation Worksheet
Use percentages, rates, and a population balance equation. Includes a worked example, printable practice, and an answer key with explanations.