Grade 11 Regression Analysis Worksheet

Grade 11 Regression Analysis Worksheet

Read each question carefully and answer to the best of your ability. Show all your work for short answer questions.

1. Which of the following correlation coefficients indicates the strongest linear relationship?

2. In a regression equation \( \hat{y} = mx + b \), what does \( \hat{y} \) represent?

3. A scatter plot shows the relationship between two   variables.

4. The   of determination, denoted by \( R^2 \), measures the proportion of the variance in the dependent variable that can be predicted from the independent variable.

5.   is the process of estimating a value outside the range of the observed data.

6. A correlation coefficient of 0 indicates a strong linear relationship between two variables.

7. The line of best fit always passes through every data point in a scatter plot.

8. Explain the difference between correlation and causation.

9. A study found a regression equation \( \hat{y} = 2.5x + 10 \), where \( x \) is the number of hours studied and \( \hat{y} \) is the predicted test score. Interpret the meaning of the slope in this context.

10. The following table shows the number of hours spent exercising per week (x) and the corresponding stress level (y) for 8 individuals (on a scale of 1-10).

Hours (x): 2, 3, 4, 5, 6, 7, 8, 9

Stress Level (y): 8, 7, 7, 6, 5, 4, 3, 2

a. Create a scatter plot for this data on the graph below.

b. Describe the direction and strength of the relationship shown in the scatter plot.

c. If the line of best fit for this data is approximately \( \hat{y} = -0.8x + 9.5 \), predict the stress level for an individual who exercises 5.5 hours per week.