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This lecture is from Statistics. Key important points are: Statistics for Business Analysis, Data and Statistics, Business and Economics, Descriptive Statistics, Statistical Inference, Numerical Facts, Art and Science, Applications In Business and Economics, Accounting Firms, Electronic Point of Sale
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Uploaded on 01/29/2013
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Regression analysis can be used to develop an equation showing how the variables are related.
Managerial decisions often are based on the relationship between two or more variables.
The variables being used to predict the value of the dependent variable are called the independent variables and are denoted by x.
The variable being predicted is called the dependent variable and is denoted by y.
The relationship between the two variables is approximated by a straight line.
Simple linear regression involves one independent variable and one dependent variable.
Regression analysis involving two or more independent variables is called multiple regression.
n The simple linear regression equation is:
n Positive Linear Relationship
y
x
is positive
Regression line
Intercept
n No Relationship
y
x
is 0
Regression line Intercept
n The estimated simple linear regression equation
y ˆ = b 0 (^) + b x 1
Least Squares Method
min (^) ∑ ( y (^) i − y ^ i ) 2
where: yi = observed value of the dependent variable for the i th observation yi^ ^ = estimated value of the dependent variable for the i th observation
Least Squares Method
Equation (^1 )
i i i
∑ ∑
where: xi = value of independent variable for i th observation
y = mean value for dependent variable
x = mean value for independent variable
yi = value of dependent variable for i th observation
Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs one or more television commercials during the weekend preceding the sale. Data from a sample of 5 previous sales are shown on the next slide.
n Example: Reed Auto Sales
n Example: Reed Auto Sales
Number of TV Ads ( x )
Number of Cars Sold ( y ) 1 3 2 1 3
Σ x = 10 Σ y = 100
y = 5x + 10
0
5
10
15
20
25
30
0 1 2 3 4 TV Ads
Cars Sold
n The coefficient of determination is:
where: SSR = sum of squares due to regression SST = total sum of squares
r^2 = SSR/SST
r^2 = SSR/SST = 100/114 =.
The regression relationship is very strong; 87.7%
of the variability in the number of cars sold can be
explained by the linear relationship between the
number of TV ads and the number of cars sold.
Sample Correlation Coefficient
2 rxy =(sign of b 1 ) r
rxy =(sign of b 1 ) Coefficient of Determinat ion
where:
b 1 = the slope of the estimated regression
