Question 1

The regression model ln(y)= β₀ + β₁x + ε is called exponential.

Accepted Answer

The model is exponential because the dependent variable y is modeled as an exponential function of the independent variable x.

Question 2

Many non-linear regression models can be studied under the linear regression framework using transformation of the response variable and/or the explanatory variables.

Accepted Answer

Transformation of variables can often make non-linear relationships between variables easier to model and analyze using linear regression techniques.

Question 3

If the data is available on the response variable y and the explanatory variable x,and the fit of the quadratic model y = β₀ + β₁x + β₂x² + ε is to be tested,standard linear regression can be applied on: A)y and x B)y,x and x² C)y,xy,and x² D)y,y² and x²

Accepted Answer

The quadratic model can be rewritten as a linear model by adding a new variable x^2.

Question 4

Although a polynomial regression model of order two or more is nonlinear,when it is fitted to the data we use the _______ regression to make this fit.
A)nonlinear
B)logistic
C)polynomial
D)linear

Accepted Answer

Although the polynomial regression model itself is nonlinear, when it is fitted to the data, we still use the concept of linear regression to make the fit. This is because the coefficients of the polynomial equation (i.e. the intercept and slopes) can still be estimated using linear regression techniques. Therefore, the best choice is D, linear regression.

Question 5

For the logarithmic model y = β₀ + β₁ln(x)+ ε,β₁/100 is the approximate change in E(y)when x increases by one percent.

Accepted Answer

In a logarithmic model, β₁ represents the elasticity of y with respect to x, meaning a 1% change in x results in an approximate β₁% change in E(y). Thus, β₁/100 is the change in E(y) for a 1% increase in x.

Question 6

The fit of the models y = β₀ + β₁x + ε and ln(y)= β₀ + β₁x + ε can be compared using the coefficients R² found in the two corresponding Excel's regression outputs.

Accepted Answer

The fit of the models cannot be compared directly using the coefficients R² as they are specific to each model and cannot be directly compared between models with different dependent variables (y and ln(y)). Other evaluation measures such as R-squared or adjusted R-squared should be used instead.

Question 7

The fit of the regression equations and can be compared using the coefficient of determination R².

Accepted Answer

The answer of The fit of the regression equations ...

Question 8

When the data is available on x and y,it is easy to estimate a polynomial regression model.

Accepted Answer

Polynomial regression is a form of regression analysis in which the relationship between the independent variable x and dependent variable y is modeled as an nth degree polynomial. When the data is available on x and y, it is possible to estimate a polynomial regression model.

Question 9

For the exponential model ln(y)= β₀ + β₁x + ε,β₁ × 100% is the approximate percentage change in E(y)when x increases by one percent.

Accepted Answer

The correct formula for the approximate percentage change in E(y) when x increases by one percent is β₁ × 100, not β₁ × 100%. The percentage change should be expressed as a decimal.

Question 10

How many coefficients have to be estimated in the quadratic regression modely = β₀ + β₁x + β₂x² + ε? A)4 B)3 C)2 D)1

Accepted Answer

In the quadratic regression model given, there are only three terms or predictors: ₀, ₁x, and ₂x². Therefore, there are only three coefficients to be estimated, and option B (3) is the correct answer.

Question 11

The fit of the models y = β₀ + β₁x + β₂x² + ε and y = β₀ + β₁ln(x)+ ε can be compared using the coefficient of determination R².

Accepted Answer

The coefficient of determination, or R-squared, measures the proportion of variance in the dependent variable that is predictable from the independent variable(s). It is a statistic used to compare the fit of different regression models, but it cannot be used to directly compare models with different independent variables or functional forms. Therefore, it is not appropriate to compare the fit of the two models in the question using the coefficient of determination.

Question 12

A quadratic regression model is a special type of a polynomial regression model.

Accepted Answer

A quadratic regression model is a type of polynomial regression model that involves fitting a second-degree polynomial equation to the data.

Question 13

The fit of the models y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε can be compared using the coefficient of determination R².

Accepted Answer

The answer of The fit of the models y =...

Question 14

Which of the following is a quadratic regression equation?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which of the following is a quadratic...

Question 15

The curve representing the regression equation has a U-shape if b₂ > 0.

Accepted Answer

A U-shaped curve in a regression equation indicates a non-linear relationship between the variables, and the coefficient of the squared term (b₂) determines the direction and magnitude of the curve. A positive value of this coefficient indicates an upward curve, which is U-shaped.

Question 16

The cubic regression model,y = β₀ + β₁x + β₂x²+ β₃x³ + ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

Accepted Answer

The cubic regression model y = β₀ + β₁x + β₂x²+ β₃x³ + ε can capture relationships between x and y that have both a minimum and a maximum.

Question 17

Which of the following regression models is not polynomial? A)y = β₀ + β₁x + ε B)y = β₀ + β₁x + β₂x² + ε C)y = β₀ + β₁x^-1 + ε D)y = β₀ + β₁x + β₂x²+ β₃x³ + ε

Accepted Answer

The third regression model does not have any terms with multiple powers of x, making it a linear model rather than a polynomial one. The other three models have at least one term with multiple powers of x, indicating that they are polynomial models.

Question 18

The equation y = β₀ + β₁x + β₂x² + ε is called a cubic regression model.

Accepted Answer

The equation is not a cubic regression model, but a multiple linear regression model with multiple terms and interactions.

Question 19

The regression model ln(y)= β₀ + β₁ln(x)+ ε is called logarithmic.

Accepted Answer

The answer of The regression model ln(y)= β₀ + β₁ln(x)+...

Question 20

For the model ln(y)= β₀ + β₁ln(x)+ ε with 0 < β₁ < 1,if x increases than E(y)increases but at a slower rate.

Accepted Answer

Since 0 < β₁ < 1, the coefficient of ln(x) is less than 1. This means that as x increases, the effect on ln(y) (and therefore y) is dampened, resulting in a slower rate of increase in E(y).

Quiz 16: Regression Models for Nonlinear Relationships

The regression model ln(y)= β0 + β1x + ε is called exponential.

Many non-linear regression models can be studied under the linear regression framework using transformation of the response variable and/or the explanatory variables.

If the data is available on the response variable y and the explanatory variable x,and the fit of the quadratic model y = β0 + β1x + β2x2 + ε is to be tested,standard linear regression can be applied on:

Although a polynomial regression model of order two or more is nonlinear,when it is fitted to the data we use the _______ regression to make this fit.

For the logarithmic model y = β0 + β1ln(x)+ ε,β1/100 is the approximate change in E(y)when x increases by one percent.

The fit of the models y = β0 + β1x + ε and ln(y)= β0 + β1x + ε can be compared using the coefficients R2 found in the two corresponding Excel's regression outputs.

The fit of the regression equations and can be compared using the coefficient of determination R2.

When the data is available on x and y,it is easy to estimate a polynomial regression model.

For the exponential model ln(y)= β0 + β1x + ε,β1 × 100% is the approximate percentage change in E(y)when x increases by one percent.

How many coefficients have to be estimated in the quadratic regression modely = β0 + β1x + β2x2 + ε?

The fit of the models y = β0 + β1x + β2x2 + ε and y = β0 + β1ln(x)+ ε can be compared using the coefficient of determination R2.

A quadratic regression model is a special type of a polynomial regression model.

The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x)+ ε can be compared using the coefficient of determination R2.

Which of the following is a quadratic regression equation?

The curve representing the regression equation has a U-shape if b2 > 0.

The cubic regression model,y = β0 + β1x + β2x2+ β3x3 + ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

Which of the following regression models is not polynomial?

The equation y = β0 + β1x + β2x2 + ε is called a cubic regression model.

The regression model ln(y)= β0 + β1ln(x)+ ε is called logarithmic.

For the model ln(y)= β0 + β1ln(x)+ ε with 0 < β1 < 1,if x increases than E(y)increases but at a slower rate.