Chapter 5

Question 1

Linear Regression and Linear Correlation

Answer 1

analyze the relationship between two quantitative variables

Question 2

Linear Regression

Answer 2

Used to analyze the relationship between two quantitative variables when one variable responds to the other, Explanatory and Response

Question 3

Linear Correlation

Answer 3

Used to analyze the relationship between two quantitative variables to determine whether a change in one variable is associated with a change in the other variable.
* So, the two variables are co-related.

Question 4

Direction

Answer 4

Positive correlation: as one variable increases, the other also increases (r has + sign)
Negative correlation: as one variable increases, the other decreases (r has ─ sign)

Question 5

Form

Answer 5

May be a straight-line relationship (linear) or curved (Here we only deal with linear)

Question 6

Strength

Answer 6

The magnitude of r indicates the strength of the linear relationship between the two
variables.
r close to -1 or 1 indicates a strong linear relationship
r close to 0 indicates no relationship or a weak linear relation

Question 7

Lurking Variable (=Extraneous Variable)

Answer 7

Variable that is hidden or not measured and that may cause a change in the measured variables

Question 8

Confounding Variable

Answer 8

Variables that have confusing effects on other variables, making it difficult to determine which might be the causal variable

Question 9

Regression equation

Answer 9

the equation of the regression line

Question 10

Analysis of Residuals

Answer 10

Regression tries to minimize the errors due to deviations not explained by the regression equation (least squares criterion)

Question 11

Residual = error (e)

Answer 11

vertical distance from the regression line to a data point (may be + or –)

Question 12

Residual Sum of Squares = Error Sum of Squares (SSE)

Answer 12

the variation in the observed values of the response variable that is not explained by the regression

Question 13

Least-squares criterion

Answer 13

Tries to minimize the Residual or Error Sum of Squares (SSE) in order to get the “best fit” line

Question 14

Predictor variable (= explanatory variable)

Answer 14

= x-variable, which can be used to make predictions about the other variable

Question 15

Response variable

Answer 15

y-variable, whose values respond to changes in the predictor variable

Question 16

Interpolation

Answer 16

using the regression equation to make predictions about the response variable, within the range of the observed values of x

Question 17

Extrapolation

Answer 17

using the regression equation to make predictions about the response variable, outside the range of the observed values of x

Question 18

The coefficient of determination (R2) = [correlation coefficient]2

Answer 18

the fraction or percentage of variation in the observed values of the response variable
that is accounted for by the regression analysis
Always: 0 ≤ R2 ≤ 1
OR 0% ≤ R2 ≤ 100%

Question 19

Population regression line (linearity) (Conditions) for Regression Inferences

Answer 19

The relationship between the two variables must be approximately linear. In other words, there are constants β0 and β1 such that, for each value x of the predictor variable, the conditional mean of the response variable is β0 + β1x.

Question 20

Equal standard deviations (homoscedasticity)
(Conditions) for Regression Inferences

Answer 20

The standard deviations of y- values must be approximately the same for all values of x

Question 21

Normal populations
(Conditions) for Regression Inferences

Answer 21

For each value of x, the corresponding y-values must be normally distributed)

Question 22

No Serious Outliers
(Conditions) for Regression Inferences

Answer 22

Significant outliers can drastically change the regression model

Question 23

Independent observations
(Conditions) for Regression Inferences

Answer 23

The observations of the response variable are independent of one another. This implies that the observations of the predictor variable not need to be independent.

Question 23

Independent observations:

Answer 23

The observations of the response variable are independent of one another. This implies that the observations of the predictor variable not need to be independent.