Linear Regression Homework

Name: Date: Period:

Linear Regression and Correlation Homework

Due Friday 11/17/17

    • No late assignments will be accepted.
    • In order to be eligible to retake the exam, you must:
        • Hand in the homework assignment on time.
        • The homework assignment must be complete.
        • The homework assignment must not have been copied.
    • The exam will be on Monday, 11/20/17
    • If you have an unexcused absence on the day of the exam, you will receive a U/0 on the exam, with no opportunity to retake the exam.

1. A regression equation for predicting the price of a car (in thousands of dollars) from fuel efficiency (in mpg) is given by .

a. Interpret the slope of the regression line in context.

b. Interpret the y-intercept in context.

c. Predict the price of a car that gets 25 miles per gallon.

d. A car used to create the regression line costs $28,000 and gets 20 miles per gallon. Find the residual for this car. Does the regression line overestimate or underestimate the data at this point?

2. Explain what a residual is. If you write a formula, explain what the parts of the formula represent.

3. Sum of squared errors

    1. Explain how SSE is calculated.
    2. What does SSE tell you about a linear model?
    3. Explain how SSE is related to the least squares regression line.
      2. 4. If the relationship between two variables is linear, what will the residual plot look like?

5. Describe the following values of the correlation coefficient in terms of strength and direction:

    1. r = -0.97
    2. r = 0.97
    3. r = -0.002
    4. r = -0.54
    5. r = 0.54

6. Convince me that you will be an informed and skeptical consumer of information in the real world by explaining what “correlation does not imply causation” means. Give an example.

7. True or False?

    1. No matter what the residual plot looks like, it always makes sense to fit a linear model to the data.
    2. If there is a strong correlation between two variables, then there is a linear relationship between those variables.
    3. If there is a strong correlation between two variables, then there is a cause and effect relationship between those variables.
    4. If there is a linear relationship between two variables, then there is a cause and effect relationship between those variables.
    5. Linear models are for making predictions.