Golly darn this

computer !!

Instructions Ex. 16.1In Excel:• File/ Open/ Folder:DataSets/ Folder:excel files/

Folder:Ch16/ Xm16-01.xls – To open data fileNote: 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

Ex. 16.2

Ex. 16.2

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!

Ex. 16.2 Assessing the model1. 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!

Ex. 16.2 Assessing the model2. 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.

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.

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

CORRELATION

• r = -0.8052• H0: ρ = 0; No linear

relationship• H1: ρ =/ 0;

Data source: Managerial Statistics, 9th Ed. (Keller)

CENGAGE