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Business 205
Review
ExamLeast Square Regression
Simple Linear Regression
Preview
Multiple RegressionTrendsForecastingExcel
Multiple Regression
Using more than one IV in order to establish the relationship to the DV.
Price and Store Location Amount Sold
r values
Correlation between variablesHow well the two or more variables are
related
Coefficient of Determination (r2)
Proportion of variation in Y that is explained by the independent variable X
SST
SSR2 r
Residuals
Estimated errors0 Difference between the observed value (Y)
and the predicted value (Yp).
pi YYe
Multiple Regression
Model a dependent variable by several independent variables
Has a constant random error “ε”
Learn about the relationship between several IVs and a DV
nno xxxy ...2211
Multiple Regression adjusted r2
Reflects both the number of independent variables in a model and the sample size
Remember:
1
111 22
kn
nrradjusted
SST
SSR2 r
ANOVA table for Regression
Source df Sum of Squares Mean Square F
Regression k SSR SSR
k
MSR
MSE
Error n – k -1 SSE SSE
n-k-1
Total n - 1 SST
Testing if the slope of the regression line is statistically significant.
What can you do with Regression?
Trends Forecasting
Excel: Regression
ToolsData Analysis
Regression
Milestone 6
Look for your “best” reliabilityCronbach’s α = .83
Find the Average for each person’s survey using ONLY those questions that are reliable
Sort data by group conditionRun your analysisWrite up the different sections
Entering it in Excel
Create a variablefor the happiness mean.
When you start runningyour statistical analyses,you will be using the HapMean score only.
Number Gender Q1 Q2 Q3 HapMean
1 F 5 4 4 4.33
2 M 3 5 2 3.33
Make sure the survey is reliable.
Take the mean of the questions and only those questions that are reliable. This becomes the “happiness” score for that person.
Write up your Methods Section
You need an Independent Variables Section and a Dependent Variables Section
IV: Money a student makesDV: Satisfaction with tuition levels
IV write up
Independent Variables
Money a student makes. The independent variable was manipulated by two groups: those who made less than or equal to $10,000 a year (n = 2) and those that made more than $10,000 a year (n = 3).
DV write up
Dependent VariablesSatisfaction with tuition levels. A 5 point Likert-type scale was utilized in order to measure satisfaction. Questions were “I believe that we are paying too much for tuition,” “States should fund more money to schools,” and “We should all protest tuition hikes” (Cronbach’s α =.83).
*Only include those questions with that reliability!
Method Section
Study Write-upA quick paragraph on how you conducted
the studySince we “cheated”, you can make it up as if you
really did do the study
Demographic Section If you have demographic/categorical data,
report it in this section
Method Section Example (Study)
Participants (N = 5) were asked to complete a survey in class regarding how they felt about tuition hikes. Participants were randomly assigned to one of two conditions: they made $10,000 or less (n = 2) or they made more than $10,000. After they completed the survey, they were thanked and were free to leave.
Excel Countif Function
=Countif(range, criteria)
=countif(A1:A4, “f”)
=countif(A1:A4, “m”)
Descriptive Statistics
Tools Data Analysis
Descriptive Statistics
Be very careful with the output as it only counts how many are there, not how many are in each category within a group!
Additionally, if you dummy code (0/1), it will take a mean of the dummy coded values!
Method Section Example (demographics)
The sample (N = 5) consisted of 40% males and 60% females with an average age of 24 (M = 24.00, SD = 1.23). Participants were predominantly Caucasian (n = 4) and had stated that they drove to work (n = 3).
Results Section (no significance)
A two independent sample t-test was conducted to see if there was a difference between amount of money a student made and how satisfied they were with a tuition hike. The results revealed no significance.
Results Section (significance)
A two independent sample t-test was conducted to see if there was a difference between amount of money a student made and how satisfied they were with a tuition hike. The results revealed significance, t(4) = -3.00 , p < .05, two-tailed.
Group Work
Have your things ready:SurveyPrint out of dataReliabilityHypothesis
What test will you need to run?
The following are formulas you can use in order to find the information located in the ANOVA regression chart.
You do NOT need to perform this by hand!!! These formulas are for your own edification
Regression
Regression Sums of Squares Explained Variation for
Predicted values of Y
Error Sums of Squares Explained Variation for
Predicted values of Y
Sums of Squares Total
2)( yP MYSSR
2)( PYYSSE
2)( yMYSSTSSRSSESST
Standard Error of the Estimate
Standard deviation around the prediction line; measures variability around the prediction line
2n
SSESYX
Testing Significance
Mean Square Regression
k = number of independent variables in the regression model
k
SSRMSR
Testing for Significance
Mean Square Error
df = (n – k – 1)
1
kn
SSEMSE
Testing a Linear Regression Slope
Testing if the slope is statistically significant
MSE
MSRF