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Nonlinear Regression Functions

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Questions and Answers

What is the relationship between test scores and district income in the California data set?

Negative correlation

No correlation

Strongly positive correlation (correct)

Random correlation

What are two economic background variables used in the analysis?

Percentage of students passing tests and district population

Number of teachers per student and percentage of students graduating

District income and the size of school buildings

Average annual per capita income and percentage of district families qualifying for income assistance (correct)

Why does the scatterplot of test scores against district income show a peculiarity?

Points are uniformly distributed

Nonlinear relationship between test scores and income (correct)

Points are clustered in the middle

Most points are above the OLS line

What characterizes a nonlinear function?

Function with a variable slope depending on input values Signup and view all the answers

For the California data set, what is the median district income in terms of per person?

$13,700 per person Signup and view all the answers

What range of district income values indicates a peculiarity in the relationship with test scores?

Between $15,000 and $30,000 Signup and view all the answers

What happens when the effect on Y of a change in one independent variable depends on the value of that variable?

The population regression function becomes nonlinear Signup and view all the answers

What is an example of a nonlinear regression function where the effect on Y depends on the value of X1?

Reducing class sizes to improve test scores Signup and view all the answers

What is the difference between linear and nonlinear population regression functions?

A linear function has a constant slope, while a nonlinear function has a varying slope Signup and view all the answers

How is the nonlinear regression function in Figure 8.1b different from the linear population regression function in Figure 8.1a?

The nonlinear regression function is steeper when X1 is small and less steep when X1 is large Signup and view all the answers

Can nonlinear regression functions be considered versions of the multiple regression model?

Yes, because they are linear functions of the unknown coefficients of the population regression model Signup and view all the answers

What is an example of a nonlinear effect in everyday life?

Taking a medication Signup and view all the answers