1.7 linear regression

Question 1

the dependent variable or the explained variable

Answer 1

refers to the variable whose variation is being explained. It is typically denoted by Y

Question 2

the independent variable or the explanatory variable

Answer 2

refers to the variable whose variation is being used to explain the variation of the dependent variable

Denoted by X

Question 3

If there is only one independent variable, then the regression is known as

Answer 3

Simple Linear Regression

Question 4

If there are two or more independent variables, the regression is known as

Answer 4

multiple rergression

Question 5

The four assumptions underlying the simple linear regression model are:

Answer 5

• Linearity
• Homoskedasticity
• Independence
• Normality

Question 6

Linearity

Answer 6

The relationship between the dependent variable and the independent variable is linear

Question 7

Homoskedasticity

Answer 7

The variance of the residuals is constant for all observations

Question 8

Independence

Answer 8

The pairs (X, Y) are independent of each other. This implies the residuals are uncorrelated across observations

Question 9

Before running a regression model, an analyst states two of the underlying assumptions for linear regression analysis:

Assumption 1: The variance of the error term has an expected value of zero
Assumption 2: The independent variable is not random
What is the most accurate assessment of the analyst’s description of the assumptions that must be satisfied to draw valid conclusions from a simple linear regression model?

A
Assumption 1 and Assumption 2 are both correct

B
Assumption 1 is correct and Assumption 2 is incorrect

C
Assumption 1 is incorrect and Assumption 2 is correct

Answer 9

C
Assumption 1 is incorrect and Assumption 2 is correct

Question 10

The sum of squares total (SST), which is the total variation in Y, can be broken into two components:

Answer 10

1. Sum of squares error (SSE), which is the unexplained variation in Y
2. Sum of squares regression (SSR), which is the explained variation in Y

Question 11

Measures of Goodness of Fit

Answer 11

Measures to evaluate how well the regression model fits the data include:

• The coefficient of determination
• The F-statistic for the test of fit
• The standard error of the regression

Question 12

The coefficient of determination (a.k.a. R-squared or R^2)

Answer 12

measures the fraction of the total variation in the dependent variable that is explained by the independent variable

Question 13

F-Statistic

Answer 13

To evaluate if our regression model is statistically meaningful

Question 14

The objective of linear regression

Answer 14

to understand what explains the variation of Y, also known as the sum of squares total (SST), or the total sum of squares

Question 15

how to find the variation of Y, also known as the sum of squares total (SST)

Answer 15

E(Yi - Y_)^2

Question 16

how to find the variation of X

Answer 16

E(Xi - X_)^2

Question 17

The regression equation

Answer 17

expresses the linear relationship between X and Y

Y = b0 + b1 * X + e

b0 = the intercept

b1 = the slope coefficient of the regression line.

e = the error them, which represents the difference between the observed value of Y and its expected value from the true underlying population.

–> the difference between the expected value of Y and the value of Y in the underlying population

Question 18

The line plotted by the regression equation represents

Answer 18

he average relationship between the dependent variable and the independent variable

Question 19

The difference between the observed and estimated values of the dependent variable

Answer 19

the residual

Observed value of Y - estimated value of Y

Question 20

coefficient of determination (R^2) formula

Answer 20

SSR / SST

Question 21

In a simple linear regression with only one independent variable, the coefficient of determination is equal to

Answer 21

the square of the correlation between X and Y.

R^2 is a descriptive measure, not a statistical test.

Question 22

the F test statistic for a simple linear regression model is:

Answer 22

F = (SSR/1) / (SSE(n-2))

Question 23

The standard error of the estimate (se)

Answer 23

the square root of MSE

se = sqrt(MSE)

also known as the standard error of the regression or the root mean square error.

A smaller value indicates a more accurate regression.

Question 24

The estimated variance of a regression model’s prediction error is determined by several factors:

Answer 24

The squared standard error of the estimate, S^2e

The number of observations, n

The value of the independent variable X relative to X_

The variance of the independent variable, S^2x