Venn diagram shows (R 2 ) the amount of variance in Y that is
explained by X. Unexplained Variance in Y. (1-R 2 ) =.36, 36% R 2
=.64 (64%) Variance in Y that is explained by X Multiple Regression
Multiple regression is used to predict one Y (dependent) variable
from two or more X (independent) variables. The advantage of
multivariate or bivariate regression is Provides lower standard
error of estimate Determines which variables contribute to the
prediction and which do not. Multiple Regression b 1, b 2, b 3, b n
are coefficients that give weight to the independent variables
according to their relative contribution to the prediction of Y. X
1, X 2, X 3, X n are the predictors (independent variables). C is a
constant, similar to Y intercept. Body Fat = Abdominal + Tricep +
Thigh List the variables and order to enter into the equation 1.X 2
has biggest area (C), it comes in first. 2.X 1 comes in next area
(A) is bigger than area (E). Both A and E are unique, not common to
C. 3.X 3 comes in next, it uniquely adds area (E). 4.X 4 is not
related to Y so it is NOT in the equation. 5.The first variable in
is the variable with the highest correlation with Y. After that, it
is the next variable with the highest Part Corr with Y. Ideal
Relationship Between Predictors and Y Each variable accounts for
unique variance in Y Very little overlap of the predictors Order to
enter? X 1, X 3, X 4, X 2, X 5 Guess the Order of Entry in Stepwise
Advertising BudgetNo of Plays on RadioAttractiveness of the Band
Record Sales Advertising Budget No of Plays on Radio.182 Step 1:
Record Sales = No of Plays Step 2: Record Sales = No of Plays + Ad
Budget Step 3: Record Sales = No of Plays + Ad Budget +
Attractiveness Multicollinearity Multicollinearity was not violated
if the following were met: (1)The largest VIF < 10 (2)the
average VIF of predictors was not substantially > 1 (3)tolerance
statistics > 0.2. Record3.sav Outlier? Is the Variance Equal?
Non Linear Regression Y = X 3 3X Regress1.sav Y = (X) R 2 = 26.2%,
SEE = 3.68 The Distribution is Not Normal The Relationship between
Xs and Y is Not Linear Compute X Squared and X Cubed Non Linear
Regression Y = X 3 3X 2 + 4 Non-Linear Regression Output Non-Linear
Regression Output Y = X 3 3X Y = X 3 3X R 2 = 100%, SEE =
Assignment Assignment 1. Use the data set Regress3.sav to run a
stepwise regression. Y = X1 + X2 + X3 + X4 After completing the
linear regression compute the following non-linear terms: X3 2 and
X4 3, then run stepwise regression with the following predictors: Y
= X2 + X3 2 + X4 3 Assignment 2. Muscle Activation.sav The purpose
of this experiment was to predict the time of muscle activation
from fiber type and nerve conduction velocity. Fiber type was
identified as slow, intermediate and fast twitch. Negative values
for muscle activation indicate that the subject activated their
muscles prior to ground contact and positive values indicated that
they activated their muscles after ground contact. Use stepwise
multiple regression. Check for outliers and remove any rows
containing a standardized residual greater than 3. Check for,
normality, homogeneity of variance and multicollinearity.
