Business 205. Review Exam Least Square Regression Simple Linear Regression

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