Paired Data and Slope of Regression Lines Quiz

STATE (Ud)

We want to estimate Ud= the true mean difference (A-B) between …

PLAN (Ud)

1 sample t-int for Ud

Random → SRS of # …

Normality → n>30

DO (Ud)

x̄ ± t* (Sd/ √nd)

x̄ = sample mean difference

t* = critical value, invT

t*= invT

A=A= (1-. CI /2) +CI

df=n -2 (BIVARIATE)

INTERPRET (Ud)

We are #% confident that the int form # to # captures the true mean difference (A-B) of …

The int suggests on average the ___ is between # and # (units) higher/lower than…

(Part B, Ud) Conclude cause and effect?

Cannot make x conclusion because it is an observational studies. No treatment imposed.

(Part B, Ud) Is there CE x increased y?

Yes there is CE … because all numbers in the int are positive (or vice versa)

(Part B, Ud) Is there CE of mean difference.

There is CE of mean difference in … because 0 is not captured in the interval of # to #.

STATE (B)

We want to estimate the B= slope of the true LSRL relating ŷ= predicted … and x=….

PLAN (B)

1 sample t-interval for slope

random → 22 random …

normal → check residual dot plots for no strong skewness or outliers

linear → check scatterplot x vs y for linear relationship

equal SD → check residual plot for random scatter

DO (B)

b ± t*SEb

b= sample slope

t*=critical value, invT

t*= invT

A=A= (1-. CI /2) +CI

df=n -2 (BIVARIATE)

SEb= from chart

INTERPRET

We are #% confident the int from # to # captures the slope of the true LSRL relating ŷ= predicted … and x=…. in population

INTERPRET (SEb)

If the study was repeated many times and we got many different LSRLs, the SEb predicts the sampling variability of the same slopes in the LSRL used to predict … from …

INTERPRET (b)

For each additional x, we expect and increase of # in y, on average.

INTERPRET (s)

This is the standard deviation of residuals. This statistic measures the amount of variability in the vertical distances from the obs … to the LSRL.

(Part B B) Is the higher the x the higher the y.

There is CE based on the CI above the more you x the higher the y because all the values in the interval are positive.