Lesson 9.3

If car prices followed the regression equation below, what would you expect the car price to be (on average) a year from now? Car Price = 50,000 + (-100) × Months

$48,800.

What two assumptions need to be met to do linear regression?

(50%) That a linear relationship does exist for these two variables. (50%) That the data values are normally distributed (vertically) around the regression line.

What are the two uses of linear regression?

(50%) To explain the change in the response variable from a change of the predictor variable. (50%) To predict the value of the response variable from the value of the predictor variable.

Below is the equation of a regression line, match each symbol with its meaning. ŷ = b0 + b1x 1. The predicted value of the y-variable. 2. The y-intercept of the regression line. 3. The slope of the regression line. 4. The value of the x-variable.

1. (ŷ) 2. (b0) 3. (b1) 4. (x)

Match each use of linear regression below with the parts of the regression equation needed for that use. 1. Slope of the regression equation (b(1)). 2. y-Intercept and slope of the regression equation ((b(0),b(1)).

1. Explanation of the effect of the predictor variable on the response variable. 2. Prediction of the value of the response variable from the value of the predictor variable.

How many of each variable below is there in simple linear regression? 1. 1 2. 1

1. Response variable. 2. Predictor variable.

Which of the points below would be closest to the regression line? Point A: with residual = +150 Point B: with residual = -120 Point C: with residual = -10 Point D: with residual = +12

Point C, as it has the smallest magnitude of the residuals (-10).

What is NOT an appropriate comment because of the Scope of the Model?

Regression is good for extrapolation outside of the range of the predictor variable.

Using the regression equation below, what would be the residual for a point with the coordinates (10,80)? Weight = -12.3 + 9 × Height

Residual = +2.3 .

Using the regression equation below, what would be the residual for a point with the coordinates (24,45000)? Car Price = 50,000 + (-100) × Months

Residual = -2,600 .

In concept, what is a regression residual?

The vertical distance a data point (x,y) is from the regression line.

From a statistics standpoint, why are the values of the slope and y-intercept needed?

They summarize the relationship information in the data set.

If car prices followed the regression equation below, would you wait to buy a car or would you buy a car now? Car Price = 50,000 + (-100) × Months

Wait to buy as car prices are on average dropping $100 per month.

If a point gives the middle of a column of data values, what gives the middle of a scatterplot?

A line going through the middle of the scatterplot.

In concept, how does linear regression find the regression line?

By finding the line where the residuals of the points are the smallest.

What does the statistical method of linear regression do?

It finds the equation (slope and y-intercept) of the middle line.

What new information does linear regression give over linear correlation?

It gives the magnitude (size) of the effect of the predictor variable on the response variable.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went up two inches? Weight = -12.3 + (-9) × Height

Weight would go down 18 lbs.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went down ten inches? Weight = -12.3 + 9 × Height

Weight would go down 90 lbs.

Using the regression equation below, how much would you expect Weight (lbs) to change on average if Height (ins) went up one inch?

Weight would go up 9 lbs.