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Statistics > Chapter 14 > Flashcards

Chapter 14 Flashcards

1
Q

What is a Multiple Regression Model?

A

Models that use 2 or more independent variables to predict the value of a dependent variable.

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2
Q

What is the Multiple Regression Model w/ k independent variables?

A
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3
Q

What is the Multiple Regression Model w/ 2 independent variables?

A
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4
Q

What is the Multiple Regression Equation w/ 2 independent variables for samples?

A

Note: you use the least-squares method to compute the sample regression coefficients b0, b1, and b2 as estimates of the population parameters β0, β1, and β2.

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5
Q

What are Multiple Regression Coefficients?

A

A regression coefficient is the slope of the linear relationship between a dependent variable and a predictor variable that is independent. (b0, b1)

The slopes of multiple variables that predict the change in the dependent variable based on the change in the independent variables. (β0, β1, β2)

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6
Q

List the 3 Methods to Evaluate the overall Multiple Regression Model

A
  1. The coefficient of multiple determination (r2)
  2. The adjusted coefficient of multiple determination (r2adj)
  3. The overall F test
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7
Q

What is the Coefficient of Multiple Determination?

A

The coefficient of multiple determination represents the proportion of the variation in Y that is explained by all the independent variables.

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8
Q

How do you determine the Coefficient of Multiple Determination?

A

The coefficient of multiple determination is equal to the regression sum of squares (SSR) divided by the total sum of squares (SST)

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9
Q

What does the Coefficient of Multiple Determine indicate?

A

r2 indicates that x% of the variation in the dependent variable is explained by the variation in the independent variables.

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10
Q

What is the Adjusted r2?

A

r2adj is the coefficient of multiple determination with the added variable of the sample size.

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11
Q

How do you determine r2adj?

A
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12
Q

Why would you use the overall F test?

A

To determine whether there is a significant relationship b/t the dependent variable and the entire set of independent variables.

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13
Q

How do you determine the FSTAT of the overall F Test?

A
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14
Q

What are H0 and H1 for the overall F test?

A
  • H0: β1 = β2 = … = βk = 0*
  • H1: At least one βj ≠ 0, j = 1,2, … , k*
    • *

If you fail to reject H0, you conclude that the model fit is not appropriate.

If you reject H0, you use methods in 14.4 and 14.5 to determine which independent variables should be included in the model.

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15
Q

Review the ANOVA Summary Table for the Overall F Test

A

Decision rule is:

Reject H0 at the α level of significance if FSTAT > Fα;

otherwise, do not reject H0.

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16
Q

Residual Analysis for the Multiple Regression Model

A

Construct and analyze the following residual plots

  • Residuals versus Ŷ
  • Residuals versus X1i
  • Residuals versus X2i
  • Residuals versus time
17
Q

How do you test a hypothesis concerning the population slope?

A

For this, use the level of significance (α) and n - k - 1 degrees of freedom to determine the critical values of t. (t table)

18
Q

What is a Test of Hypothesis Concerning the Population Regression Coefficients?

A

To determine whether an independent variable, e.g. X2, has a significant impact on the dependent variable, e.g. Y, after taking into account the effect of another independent variable, e.g. X1.

H0: β2 = 0

H1: β2 ≠ 0

“At the α level of significance, is there evidence that the β2 of X2 w/ β1Χ1 is different from zero?”

19
Q

How do you determine the Confidence Interval Estimate for the Slope?

A

Construct a (e.g.) 95% confidence interval estimate of the population slope, β1, (the effect of price, X1, on sales, Y, holding constant the effect of promotional expenditures, X2), the critical value of t at the 95% confidence level with n - k - 1 degrees of freedom (using the t table)

20
Q

What is the partial F test?

A

An alternative to the t test for determining the contribution of an independent variable.

Determine the contribution to the regression sum of squares (SSR) made by each independent variable after all the other independent variables have been included in the model.

The new independent variable is included only if it significantly improves the model

21
Q

How do you Determine the Contribution of an Independent Variable to the Regression Model?

A

Note: this is for 1 independent variable

22
Q

How do you Determine the Contribution of an Independent Variable to the Regression Model? (multiple variables)

A

Note: This is for multiple variables

23
Q

How do you determine the Partial F Test Statistic?

A
  • H0:* Variable X1 does not significantly improve the model after variable X2 has been included.
  • H1:* Variable X1 significantly improves the model after variable X2 has been included.
    • *

Note: This is where you use

24
Q

P Values

Statistics (11 decks)

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