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# How to: Regression & Correlation

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Working with computer: Regression analysis & Correlation using Data Analysis Plus AddIn

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### How to: Regression & Correlation

1. 1. Instructions Ex. 16.1 In Excel: • File/ Open/ Folder:DataSets/ Folder:excel files/ Folder:Ch16/ Xm16-01.xls – To open data file Note: Variable X in the 1st column & variable Y in the 2nd column • Insert/ Chart/ Standard Types: (XY) Scatter/ Next: Specify the Input Y Range & the Input X Range/ Next/ Titles Tab – Title:____; Value (X) axis:____; Value (Y) axis:____; Finish/ - To produce Scatter Diagram • Tools/ Data Analysis / Regression/ OK/ Highlight the Input Y Range & the Input X Range/ Output Options: New Worksheet Ply/ OK - To compute the least squares regression line
2. 2. Ex. 16.2
3. 3. Ex. 16.2
4. 4. Ex. 16.2 Interpretation • The regression line is: ŷ = 17.25 – 0.0669x • The slope coefficient, b1= -0.0669, means that for each additional 1,000 miles on the odometer, the price decreases by an average of \$0.0669 thousand, i.e. each additional mile, price decreases by 6.69 cents. • The intercept, b0 = 17.25, means that when the car was not driven at all, the selling price is \$17.25 thousand @\$17,250 – most probably meaningless!
5. 5. Ex. 16.2 Assessing the model 1. Standard Error of Estimate: SSE = 0, when all the points fall on the regression line – thus, smaller SSE excellent fit! SSE =0.3265, compared with y-bar = 14.841, considered small!
6. 6. Ex. 16.2 Assessing the model 2. Testing the Slope: Step 1: H0: β1 = 0; No linear relationship (slope =0) H1: β1 =/ 0 Linear relationship exist Step 2: Student t distribution with Degrees of freedom, ν= n -2; Step 3: Test Statistic for β1 (formula) @ b1 ± tα/2sb1 b1 = -13.44 with p-value≈0 (very small). Step 4: There is significance evidence to infer that a linear relationship exist. Step 5: The odometer reading may affect the selling price of cars.
7. 7. Ex. 16.2 Assessing the model • Define: Coefficient of Determination - a measure of the strength of the linear relationship: R2 = 0.6483 • It means, 64.83% of the variation in the selling prices is explained by the variation in the odometer readings. The remaining 37.17% is unexplained. • In general, the higher the value of R2, the better the model fits the data.
8. 8. Cause & Effect: Coefficient of Correlation • • • • Population coefficient of correlation, ρ (rho) Sample, r ( -1< r <1) Formula: Tools/ Data Analysis Plus/ Correlation (Pearson)/ Variable 1 Range/ Variable 2 Range/ OK
9. 9. CORRELATION • r = -0.8052 • H0: ρ = 0; No linear relationship • H1: ρ =/ 0;
10. 10. Data source: Managerial Statistics, 9th Ed. (Keller) CENGAGE