Residuals and Causation

The height of a plant is measured each week after the first sprout shows above the soil. A botanist tries to predict the height of the plant in the upcoming weeks using the observed data in the table below. Which week has the smallest residual value?

• 1

• 3

• 4

• 6

The table below shows the number of chickens on a farm in different years. What is the residual value for the year 2007?

• 0.8

• 0.5

• -0.2

• -0.3

When calculating the linear model (which is the equation for the Line of Best Fit for a set of quantitative data) our goal is to...

• Minimize the residuals

• Maximize the residuals

• Ignore the residuals

• What are residuals?

What is the "error" or the how off your predicted value is from your actual value?

• Residual

• Correlation

• Causation

• Error

Residuals are . . . 

• possible models not explored by the researcher

• variation in the response variable that is explained by the model

• the difference between the observed response and the values predicted by the model

• data collected from individuals that is not consistent with the rest of the group

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

• YES

• NO

After performing analyses on a set of data, Mrs. Schoeneck examined the scatter plot of the residual values for each analysis. Which scatter plot indicated the best linear fit for the data?

• A

• B

• C

Based on the residual plot would you say the regression line is a pretty good fit?

• Yes

• No

• Maybe

• Need more info

Which graph indicates the model for the data is a good fit?

• Graph A

• Graph B

“Least-squares” in the term “least-squares regression line” refers to...

• Minimizing the sum of the squares of all values of the explanatory variable.

• Minimizing the sum of the squares of all values of the response variable.

• Minimizing the products of each value of the response variable and the predicted value based on the regression equation.

• Minimizing the sum of the squares of the residuals.