The University of Tennessee, Knoxville

BAS BAS-320

Permutation procedure:
No Yes Discrepancy Est p-val
Avg (ANOVA) 57.77 59.77 21.2 0
Mean.Ranks(Kruskal) 4096 3977 18.11 0
Medians 58 61 13.26 0
With 500 permutations, we are 95% confident that
the p-value of ANOVA (means) is between 0 and 0.007
the p-value of Kruskal-Wallis (ranks) is between 0 and 0.007
the p-value of median test is between 0 and 0.007
**look at mean (close together, looks normal), or median (skew,
outliers, etc)
-there is significance (>0.05) but there is inconclusive bc 0—so run
more permutations
-practical significance: difference of means/median (whichever u chose
in (a)) small, point out difference and give insight
2) Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.56 0.35 10.17 <2e-16 ***
RecentAvgAmount 0.86 0.02 43 <2e-16 ***
Residual standard error: 8.555 on 2025 degrees of freedom
Multiple R-squared: 0.48, Adjusted R-squared: 0.47
F-statistic: 1871 on 1 and 2025 DF, p-value: < 2.2e-16
**P-VALUE: significant (F); RESIDUAL (actual-predicted): 8.555
-use Multiple R square for variation
SLOPE INTERPRETATION: Two observations that differ in x (context)
are expected to differ in y (context) by slope. The person who has a
higher x (context) is expected to have a lower/higher y (context). (IF
Multiple linear-all other x held constant)
INTERCEPT INTERPRETATION: Among observations where x (context) is
equal to 0, we expect on average to observe y (context) of intercept. (if
multiple: all other x held constant)
-- if you compare 2 people who differ in x by whatever amount, how
much does model suggest their y will differ: (slope times the number)
CONFIDENCE INTERVAL of slope: slope +/- 2(standard error)
CONFIDENCE INTERVAL of intercept: intercept +/- 2(standard error)
**predicting how much someone will have---- look at units
***Predictions that have more uncertainty normally have higher x
values, so they are further from the mean of x
**if person increases their x from previous problem, nothing happens
to their y because model is not physical law—can’t make predictions
about person’s change in x
-EXTRAPOLATION: outside of bounds of model-may not be trustworthyno guarantee it will remain linear
-EXTREME OUTLIERS: use log or log/log to bring in extreme outliers to
help create normal
--finding transformations:
^LastAmount0.5=0.745+0.84RecAvgAmt0.5
RecAvgAmt0.5
0.745+0.84¿
¿^
LastAmount=¿
**which conditions pass: p-value greater than .05
-when n>25, check diagnostic plots
B and c are good graphs for residual plots, a: heteroscedasticity, and d:
unequal spread
**correlation does not cause causation
All models are wrong, but some are useful- George Box
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.680805 0.361894 10.171 <2e-16 ***
RecentAvgAmount 0.871514 0.081371 10.780 <2e-16 ***
TotalAmount -0.002257 0.001800 -1.253 0.21
Residual standard error: 8.655 on 2024 degrees of freedom
Multiple R-squared: 0.4807, Adjusted R-squared: 0.46
F-statistic: 936.7 on 2 and 2024 DF, p-value: < 2.2e-16
SSE reduction: if it is not significant, adding it in the multiple regression
does not significantly increase/decrease (depending on sign of estimate)
the sum of squares error
a) If you build a 95% confidence interval for the coefficient of
Total Amount, what value will be contained in this interval?
When this value is in a 95% confidence interval for the
coefficient of a predictor in a regression model the p-value will
be above 0.05.
0
 (5) ___________ (Yes or No) Could total amount contain
information about Last Amount?
 Why total amount might have info in simple linear
regression but not multiple? Info it contains is already
being explained by recent average amount—
multicollinearity.
Which is better: multiple regression or simple linear: simple because
adjusted r square is .01 lower and RMSE (size of error) is .1 worse in
multiple regression.
***not everything that is significant in multiple linear regression is
significant in simple