The University of Tennessee, Knoxville

BAS 320

Association:
Knowing the value of x tells you something about the possible values of y
Correlation:
The expected difference in y between two individuals is proportional to the difference in x
Examining Association:
Mean/Standard Deviation - when distribution of y is roughly symmetric with no outliers
Median - when distribution is noticeably skewed or has outliers
Average - compared when typical value of y is summarized well
When to use boxplot, mosaic plot, scatterplot, etc:
Boxplot – Y-value is quantitative and X-value is categorical
Mosaic plot – Y value is categorical and X value is categorical
Scatterplot – Y value is quantitative and X value is quantitative
When to Use Pearson/Spearman:
Pearson – Linear relationship and point cloud is wide
Spearman – non-linear relationship, 1 direction, and has outliers
What standard error and RMSE tell us:
Standard Error – That our estimated slope of is likely off from the truth by about or so.
RMSE - tells us that the typical error made by the regression is (i.e. points are away
from the line.
Invalid model because of a negative intercept, why not?:
The intercept tells us the average value of y when x=0. There are no people with 0 x so this is meaningless.
What least squares does:
Minimizes the sum of the squared errors
Assumptions:
If p-value is > 5% it passes
If p-value is < 5% check diagnostic plots only if n>25
F-test for linearity:
If p-value > 5% the test is passed and we can consider the relationship to be linear
Test for equal spread:
If p-value is > 5% the test is passed and we can consider the stream of points to have equal spread
Test for normality:
If p-value is > 5% the test is passed and we can consider the residuals normal
Regression Equation:
Intercept + Slope * Value
Implicit Regression Equation:
Intercept + Slope(x) +Slope(x)…. *(given)
Simple Linear Regression Significance:
For a variable to be significant in a simple linear regression but not in a multiple regression must mean
that the information it provides about y is redundant with the information provided by the other variables
in the multiple regression.
For a variable to be non-significant in a simple linear regression but significant in a multiple regression
probably means the information it provides about y is overshadowed by the information provided by
another variable. Once that variable is accounted for, the association between y and the predictor can now
be glimpsed.