Chapter 7: Linear Regression Models

Question 1

Linear Regression Equation

Answer 1

ŷ = a + bx
ŷ = predicted y-value
a = y-intercept
b = slope

Question 2

Extrapolation

Answer 2

Predictions made outside of the interval of current data’s x-values (often not reliable)

Question 3

Residual

Answer 3

The difference between the actual response value and the model’s predicted response value (y-ŷ)
Positive = underestimation
Negative = overestimation

Question 4

Residual Plot

Answer 4

Visualizes and accentuates the residuals, allowing us to assess our model’s fit

Question 5

Good Fit Vs. Bad Fit For Residual Plots

Answer 5

Good: Apparent randomness, centered at 0, no clear patterns
Bad: Curved pattern

Question 6

Line Of Best Fit

Answer 6

The line that minimizes the sum of the squares of the residuals
(Contains mean)

Question 7

Coefficient Of Determination (r^2)

Answer 7

The percentage of variation in the response variable that is explained by the explanatory variable in the model
“____% of the variation in response variable can be explained by the linear relationship with explanatory variable.”
(0<=r^2<=1)
Closer to 0 = Weaker
Closer to 1 = Stronger

Question 8

Reading Computer Regression Tables (LSRL)

Answer 8

Column 2, Row 2 = y-intercept = a
Column 2, Row 3 = slope = b
Column 1, Row 3 = x variable
Row 4, Value 1 = SD of residuals
Row 4, Value 2 = r^2 in % form

Question 9

Residual Interpretation

Answer 9

“The actual [y-context] was [residual] [above/below] the predicted value when [x-context] = [#].”

Question 10

Slope Interpretation

Answer 10

“The predicted [y-context] [increases/decreases] by [slope] for each additional [x-context].”

Question 11

y-Intercept Interpretation

Answer 11

“The predicted [y-context] when [x=0 context] is [y-intercept].”

Question 12

Standard Deviation Of Residuals (s) Interpretation

Answer 12

“The actual [y-context] is typically about [s] away from the value predicted by the LSRL.”