Download Statistics: Scatter Plots, Correlation and Regression Analysis and more Quizzes Business Statistics in PDF only on Docsity!
Scatter Plot
can be used to show the relationship between two variables TERM 2
Correlation Analysis
DEFINITION 2 is used to measure the strength of the association (linear relationship) between two variables TERM 3
Regression Analysis
DEFINITION 3 used to predict the value of a dependent variable based on the value of at least one independent variableexplain the impact of changes in an independent variable on the dependent variable TERM 4
Dependent Variable
DEFINITION 4 the variable we wish to predict or explain TERM 5
Independent Variable
DEFINITION 5 the variable used to predict or explain the dependent variable
Simple Linear Regression Model
- only one independent variable, x-relationship between x and y is described by a liner function-changes in Y are assumed to be related to changes in X TERM 7
Types of Relationships
DEFINITION 7 LinearCurvilinear TERM 8
Y= Bo + BiXi + Ei
DEFINITION 8 y= dependent variableBo= population, y interceptBi=population slope coefficientXi=independent variableEi=random error term TERM 9
Simple Linear Regression Equation
DEFINITION 9 provides an estimate of the population regression line TERM 10
Finding the Least Squares Equation
DEFINITION 10 The coefficient Bo and Bi and other regression results in this chapter, will be found using Excel
The standard deviation (standard error)
around the regression line is estimated by
Syx=sqrt(SSE/n-2) TERM 17
Assumptions of Regression L.I.N.E
DEFINITION 17 Linearity-The relationship between x and y is linearIndependence of Errors-Error values are statistically independentNormality of Error-Error values are normally distributed for any given value of XEqual Variance (homoscedasticity)-The probability distribution of the errors has constant variance TERM 18
Inferences About the Slope:
tTest
DEFINITION 18 Is there a linear relationship between X and Y? TERM 19
Null Hypothesis
DEFINITION 19 Ho: Bi=0 (no linear relationship) TERM 20
Alternative Hypothesis
DEFINITION 20 Hi: Bi does not equal 0
tTest
tstat= bi-Bi/ Sbidf= n-2bi-regression slope coefficientBi- hypothesized slopeSbi-standard error of the slope TERM 22
Are individual variables Significant?
DEFINITION 22 Use t tests of individual variable slopesShows is there is a linear relationship between the variable Xj and Y holding constant the effects of other X variablesHypotheses:Ho: Bj= ( no linear relationship)Hi: Bj does not equal 0 (linear relationship does exist)
