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?

<p>Function with a variable slope depending on input values (B)</p> Signup and view all the answers

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

<p>$13,700 per person (B)</p> Signup and view all the answers

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

<p>Between $15,000 and $30,000 (D)</p> 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?

<p>The population regression function becomes nonlinear (A)</p> 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?

<p>Reducing class sizes to improve test scores (A)</p> Signup and view all the answers

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

<p>A linear function has a constant slope, while a nonlinear function has a varying slope (B)</p> 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?

<p>The nonlinear regression function is steeper when X1 is small and less steep when X1 is large (D)</p> Signup and view all the answers

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

<p>Yes, because they are linear functions of the unknown coefficients of the population regression model (B)</p> Signup and view all the answers

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

<p>Taking a medication (B)</p> Signup and view all the answers

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