Transformations to Achieve Linearity

• There is a linear relationship between x and y, and Regression I yields a better fit.

• There is a linear relationship between x and y, and Regression II yields a better fit.

• There is a negative correlation between x and y.

• There is a nonlinear relationship between x and y, and Regression I yields a better fit.

• There is a nonlinear relationship between x and y, and Regression II yields a better fit.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

• Model A is appropriate, since the relationship between x and y is linear.

• Model B is appropriate, since the relationship between x and y is linear.

• Model A is appropriate, since the relationship between log x and log y is linear.

• Model A is appropriate, since the relationship between log x and y is linear.

• Model B is appropriate, since the relationship between x and log y is linear.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

A linear regression analysis of the cost of tuition at a typical four-year private college versus year (from 1976 through 2008) produced the residual plot to the right.

3. Based only on this residual plot, which of the following statements must be true?

I. The relationship between tuition cost and year is non-linear.

II. Tuition cost decreased from 1976 through 1982.

III. This regression equation would underestimate tuition cost in 1992.

• I only

• II only

• III only

• I and III are true.

• None of these statements are true.

Tags

CCSS.HSS.ID.B.6B

A linear regression analysis of the cost of tuition at a typical four-year private college versus year (from 1976 through 2008) produced the residual plot to the right.

4. The scatterplot of Log (Tuition cost) versus Year shows a strong, positive, linear pattern. Which one of the following conclusions can be drawn from this information?

• The scatterplot of Log (Tuition cost) versus Log (Year) will also be strong, positive, and linear.

• The residual plot for the regression of Log (Tuition cost) on year will show a curved pattern similar to the one shown above.

• The relationship between Tuition cost and Year can be modeled well by a square root function.

• The relationship between Tuition cost and Year can be modeled well by an exponential function.

• The relationship between Tuition cost and Year can be modeled well by a power function.

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

Below is the computer regression analysis of the relationship between Log (tuition cost) and year.

Predictor Coef SE Coef T P

Constant -51.055 2.997 -17.03 0.000

Year 0.027699 0.001505 18.40 0.000

S = 0.0507261 R-Sq = 97.1% R-Sq(adj) = 96.8

Which of the following is the correct regression equation from this analysis?

• Predicted Cost = -51.055 + 0.0277(Year)

• Predicted Cost = -51.055 + 0.0277(logYear)

• Predicted logCost = -51.055 + 0.0277(Year)

• Predicted logCost = -51.055 + 0.0277(logYear)

• Predicted logCost = 0.0277 - 51.055(logYear)

Tags

CCSS.HSS.ID.B.6A