Residuals

R Squared

Slope

y-intercept

Using the Equation

100

You buy a house that is undervalued given the local market's predictions for price versus size. Would this be a positive or negative residual?

Negative

100

Two variables have a correlation of -0.89. What is the R-squared?

0.7921

100

What is the equation for the slope?

b1 = r(Sy/Sx)

100

What is the equation for the y-intercept?

b_{0}= average y - b_{1}(average x)

100

Given the linear equation: Predicted Sales = 5,424 + 391Number of Sales People Working. If 3 people are working, what would you expect the sales to be?

$6,597.00

200

Your data provides a predicted value of 58.74 and an observed value of 98.12. Does your model overestimate or underestimate the value at this point? Why?

Underestimate - the predicted value is below the observed.

200

Graph A has an R-squared of 0.38. The slope is positive. What is the value of the correlation coefficient?

r=.616

200

You're given a correlation of -0.32. What does this tell you about the slope?

The slope will be negative.

200

Given the linear regression of Height (y) versus Shoe Size (x) and regression equation Predicted Height = 25 + 3.9Shoe Size. Is the y-intercept of 25 inches tall meaningful?

No, because no one has a shoe size of zero.

200

Given the equation of Years Since 2008 versus Number of Fires in the Framingham area: Predicted Number of Fires = 4,832 + 10.35Year Since 2008. If in 2010 there were 3,915 fires, what is the residual?

-937.7

300

Given the regression model, Predicted Potassium = 38 + 27Fiber, for 20 cereals in terms of fiber versus potassium, what does it mean to say that a certain cereal has a positive residual?

That the predicted potassium is less than the observed.

300

The correlation between a cereal's fiber and potassium is r=0.903. What percent of the variability in potassium is accounted for by the fiber?

0.8154

300

The regression model of Predicted MPG = 46.87 - 0.084 Horsepower relates cars' horsepower to their fuel economy (in MPG). Explain what the slope means.

For every increase in horsepower, the predicted fuel economy goes down 0.084 MPG.

300

If you had a regression comparing Math SAT scores and Verbal SAT scores, would the y-intercept have meaning?

Yes, someone could get a zero on one section and a better score on the other.

300

Given the linear regression of 50 students at a local middle school for Average Daily Calorie Intake (in hundreds of calories) versus Waist Size of: Predicted Waist Size = 25 + 0.587Average Daily Calorie Intake. A person who generally takes in 3,500 calories a day would have what predicted waist size?

45.545

400

The regression model of Predicted MPG = 46.87 - 0.084 Horsepower relates cars' horsepower to their fuel economy (in MPG). If you have a car with 200 horsepower and 36mpg. How far off is the predicted value?

5.93mpg

400

The regression model of Predicted MPG = 46.87 - 0.084 Horsepower relates cars' horsepower to their fuel economy (in MPG). Which of the following is the likely r-value?

A. 46.87

B. .084

C. 1

D. -.6

E. -1

D. -.6

400

Predicted Potassium = 38 + 27Fiber. This is the linear model for fiber (in grams) and potassium (in milligrams). Explain what the slope means.

For every gram increase in fiber, predicted potassium goes up 27 milligrams.

400

An analysis of Age (in years) versus Total Weekly Purchases (dollars) generates the linear model of Predicted Purchases = 539.803 + 1.103Age. Is the y-intercept meaningful?

No, a zero year old person cannot make purchases.

400

A person tells you their Math SAT score was 500. Predict their Verbal score using the linear model of Predicted Verbal SAT Score = 171.333 + 0.6943Math SAT Score.

518.483

500

Given the regression model: Predicted Verbal SAT Score = 171.333 + 0.6943Math SAT Score. Would you rather have a positive or negative residual?

Positive - you always want a higher score than the predicted.

500

The coefficient of determination is 71.49%. What is the correlation coefficient if the LSRL is Bank Account Balance = -48*Days Since Payday + 584

-.845

500

If there was a linear model of potassium versus fiber and the units of potassium were changed from milligrams to grams, would this affect the slope or the correlation?

The slope. Correlation has no units.

500

You have a y-intercept of 387 for the linear regression Predicted Calorie Intake from Food = 387 + 45.8Number of Meals Eaten per Day. This y-intercept has meaning. True or false.

False, when you eat zero meals, you consume 0 calories.

500

Given the equation Math SAT Score = 209.5542 + 0.67507Verbal SAT Score for a regression analysis of a local high school's SAT scores. Every year a student scores a percent 1600. Based on the model, what would be that student's Math score residual?

50.3898