data analysis: summary and ANOVA tables

Question 1

p≥0.1

Answer 1

no evidence against null hypothesis

Question 2

0.01≤p≤0.1

Answer 2

low/moderate evidence against null hypothesis

Question 3

0.001≤p≤0.01

Answer 3

strong evidence against null hypothesis

Question 4

p<0.001

Answer 4

very strong evidence against null hypothesis

Question 5

how can we determine whether our model is good from the summary(model) output

Answer 5

a good model has 0≤R²≤1 as close to 1 as possible

Since if R² = 1 then SSR/SST = 1 which implies SSE = 0. Then eᵢ = 0 for all I so we say the model has a “perfect fit”

Question 6

how can we determine MSE (mean square error) from the summary(model) output?

Answer 6

MSE = “residual standard error”²

Question 7

how can we determine R² from the summary(model) output?

Answer 7

R² = “multiple R-squared” = SSR/SST

Question 8

β₀ is always the ….

Answer 8

…. intercept

Question 9

how would you determine a confidence interval from the summary(model) output?

Answer 9

estimate ± c.v (standard error)

note: c.v = t(ɑ/2),(n-2) and can be looked up using t-tables

Question 10

how can the F-stat calculated for ANOVA be verified

Answer 10

F-stat is part of the output in summary(model)

note that k and n-p are also outputted here

Question 11

how do we calculate F from anova(model)?

Answer 11

MSR/MSE

Question 12

how do we calculate DF from anova(model)?

Answer 12

DF for regression = k (given as part of summary(model) )

DF for error = n-p (given as part of summary(model) )

total DF is always n-1

Question 13

how do we calculate SSR from anova(model)?

Answer 13

sum sq for x1 + sum sq for x2

Question 14

how do we calculate SSE from anova(model)?

Answer 14

sum sq for residuals

Question 15

how do we calculate SST from anova(model)?

Answer 15

SSR + SSE

Question 16

how do we calculate MSR from anova(model)?

Answer 16

SSR/DF (regression)

Question 17

how do we calculate MSE from anova(model)?

Answer 17

SSE/DF (error)

Question 18

what is the definition of SSR

Answer 18

measure of how well our line fits the data

Question 19

how do we interpret SSR

Answer 19

higher SSR, better model fit

Question 20

what is adj R squared

Answer 20

adjusting for number of variables in regression. more variables can make R²adj lower

Question 21

what is the definition of SSE

Answer 21

measure of how much of the variability is in the error term

Question 22

what is the definition of SST

Answer 22

dispersion of the observed variables around the mean

Question 23

what is the definition of MSE

Answer 23

averaged squared difference between the estimated values and actual values

Question 24

how do we interpret MSE

Answer 24

greater MSE, less likely the regression is significant

Question 25

how do we interpret F

Answer 25

large values of F support the conclusion that the overall relationship is statistically significant