Leonardo da Vinci, the renowned painter, speculated that an ideal human would have an armspan (distance from the outstretched fingertip of the left hand to the outstretched fingertip of the right hand) that was equal to his height. Is it possible to predict armspan from height? The following computer regression printout shows the results of a least-squares regression of armspan on height, both in inches, for a sample of 18 high school students. The students’ armspans ranged from 62 to 76 inches. Which of the following statements is true? (click on the picture to enlarge)

If one of the students in the sample had a height of 70 inches and an armspan of 68 inches, then the residual for this student would be about –2.36 inches.

The correlation between height and armspan is .871.

Contrary to da Vinci’s speculation, the regression model suggests that, for these students at least, height is about 84% of armspan.

For every one-inch increase in armspan, the regression model predicts about a 0.84-inch increase in height.

For a student 66 inches tall, this model would predict an armspan of about 68 inches.

You are interested in predicting the cost of heating houses on the basis of how many rooms the house has. A scatterplot of 25 houses reveals a strong linear relationship between these variables, so you calculate a least-squares regression line. “Least-squares” refers to

Minimizing the sum of the squares of the residuals.

Minimizing the sum of the squares of the 25 houses’ heating costs.

Minimizing the sum of the squares of the number of rooms in each of the 25 houses.

Minimizing the sum of the products of each house’s actual heating costs and the predicted heating cost based on the regression equation.

Minimizing the sum of the squares of the difference between each house’s heating costs and number of rooms.

Residual Calculations Quiz

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Math

Probability And Statistics

Residuals

Residual Calculations

Authored by Anthony Clark

Mathematics

11th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

1 min • 1 pt

How do you calculate a residual?

Observed - Predicted

Predicted - Observed

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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?

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

YES

MULTIPLE CHOICE QUESTION

1 min • 1 pt

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

YES

FILL IN THE BLANK QUESTION

1 min • 1 pt

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Residual Calculations

How do you calculate a residual?

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?

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

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

The regression equation y = 25x + 100 models the cost, y, of an event for x people. The table shows what the party sizes actually paid. Complete the table with the predicted values and residuals.

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