Understanding Regression Terminology and Simple/Multiple Linear Regression

Statistics
Name:
Institution:
2nd June 2018

Part 1 – Understanding Regression Terminology
 R2 versus Adjusted R2; the adjusted R2 is basically a modified version of R2 that has been
adjusted for the number of predictors in the model. The adjusted R2 increases if and only
if the new term improves the model more than would be expected by chance.
 Beta; this is a measure of volatility of a stock
 Regression coefficient; this is the constant ‘b’ in the regression equation that indicates the
change value in the dependent variable that corresponds to the unit change in the
independent variable.
 Hierarchical regression; this is a regression model that is used to show if variables of
interest explain a statistically significant amount of variance in the Dependent Variable
(DV) after accounting for all other variables.
 Multi-collinearity; refers to a phenomenon where one independent variable in a multiple
regression model can be linearly predicted from the other independent variables with a
substantial degree of accuracy.
 Curvilinear; refers to a smooth curve like a parabola or logarithmic curve.
 Homoscedasticity; refers to a situation where the variance around the regression line
(error term) is the same for all values of the predictor variable (X).
 Outlier; refers to an observation point that is way away or distant from other
observations.
 Residual; refers to the difference between the observed value of the dependent variable
(y) and the predicted value (ŷ).
Part 2 – Simple Linear Regression

The regression output is given below;
From the output we can say that the results are significant. The interview score (x1) is
statistically significant (p < 0.05).
The least square regression line is;
y=0.5122 x +1.4443
Estimation of Jeff’s performance. The interview score is 3.4 hence the performance would be;
y=0.5122∗3.4 +1.4443=3.18578
Part 3 – Multiple Regression
The organization wants to use a combination of interview scores (x1), scores from a role playing
exercise (x2), and personality test scores (x3) to predict performance (y) in the employee
development program. An I/O psychologist collected data on the 32 employees who have already
participated in the program.
1. Run a multiple regression analysis in Excel.