# Question: It is possible to adapt some of the tools used

It is possible to adapt some of the tools used in linear regression to certain nonlinear cases. Suppose, for example, you wanted to link independent variable x to dependent variable y using the following data. The scatter diagram for the data is provided.

The data here appear to suggest a nonlinear relationship, perhaps a power function, connecting x to y. (A power function has the general form y = cxq, where c and q are constants.) To fit a power function, we could linearize the data by computing the natural log of the x and y values, then use linear regression to find the slope and the intercept of the least squares line that best fits the transformed data. The transformed data and the associated scatter diagram are shown below:

Taking the natural log of both sides of the y cx q equation gives ln(y) ln (c) + qln (x), showing ln (y) as a linear function of ln (x).

a. Find the least squares line that best describes the transformed data.

b. Report the appropriate c and q values for the associated power function.

c. Use the power function that you’ve identified to compute the expected value of y for x = 5. For x = 11.

The data here appear to suggest a nonlinear relationship, perhaps a power function, connecting x to y. (A power function has the general form y = cxq, where c and q are constants.) To fit a power function, we could linearize the data by computing the natural log of the x and y values, then use linear regression to find the slope and the intercept of the least squares line that best fits the transformed data. The transformed data and the associated scatter diagram are shown below:

Taking the natural log of both sides of the y cx q equation gives ln(y) ln (c) + qln (x), showing ln (y) as a linear function of ln (x).

a. Find the least squares line that best describes the transformed data.

b. Report the appropriate c and q values for the associated power function.

c. Use the power function that you’ve identified to compute the expected value of y for x = 5. For x = 11.

**View Solution:**## Answer to relevant Questions

Suppose you suspect an exponential relationship between independent variable x and dependent variable y. (An exponential relationship has the general form y = mqx, where m and q are constants.) You want to use simple linear ...The output below is from a multiple linear regression analysis done by an area realty group. The analysis is intended to link y, the time that a house listed for sale remains on the market, to the size of the house (x1), the ...Below are results from a regression analysis attempting to link a dependent variable y to independent variables x1 and x2. a. Can these results be used to reject the “all βs are 0” null hypothesis at the 5% significance ...Below is output from a regression analysis attempting to link dependent variable y (productivity) to independent variables x1 (training time) and x2 (experience) using a sample of 20 assembly operators at Jensen ...As transportation manager at ABC Manufacturing, you are trying to determine whether there is a useful linear relationship between x, the distance that your product is shipped, and y, the amount of damage reported by ...Post your question