Chapter 26: Inference for Regressions

Question 1

Sample Regression Line

Answer 1

LRSL ŷ=a+bx computed from sample data

Question 2

Population Regression Line

Answer 2

LSRLμy=α+βx based on the entire population of data

Question 3

Sampling Distribution Of Slope b

Answer 3

Choose a random sample of n observations (x,y) from a population of size N with LSRL y=α+βx

Question 4

Mean & Standard Deviation Of Linear Regression Distribution

Answer 4

μb=β
σb=σ/(σx[squareroot{n}])

Question 5

Regression Inference Conditions

Answer 5

Linear - no curvature in residuals
Independent - n≤10% of pop.
Normal - no strong skewness or outliers or n≥30 (CLT)
Equal SD - standard deviation of y is the same for all values of x
Random - random sample

Question 6

Computer Output (How To Read)

Answer 6

2nd Row, 2nd Column = y-intercept
3rd Row, 2nd Column = slope
3rd Row, 3rd Column = SE
3rd Row, 4th Column = test statistic
3rd Row, 5th Column = p-value

Question 7

LinRegTInt Interpretation

Answer 7

“We are [C%] confident that the interval between [A and B] captures the slope of the population regression line relating [x in context] to [y in context].”

Question 8

LinRegTInt On Calculator

Answer 8

Xlist: List of x-values on L1
Ylist: List of y-values on L2
Freq: 1
C-Level: CI% as a decimal
RegEQ: (Leave blank)

Question 9

Degrees Of Freedom Regression

Answer 9

df=n-2

Question 10

LinRegTTest p-value Interpretation

Answer 10

“Assuming [H0 in context] is true, there is a [p-value] probability of getting a sample regression line with a slope as extreme as the one in the study or more extreme, by chance alone.”

Question 11

Standard Error Of The Slope Interpretation

Answer 11

“The slope of the sample LSRL for [x-context] and [y-context] typically varies from the slope of the population LSRL by about [SEb].”