A state attornmey general is investigating the possibility of collusive bidding

Question

A state attornmey general is investigating the possibility of collusive bidding among the state's road construction contractors. One aspect of the investigation involves a omparison of the number of contractors bidding on a job and the resultant winning lowest) bid price. The sample data shown below were supplied by the state's Department of Transportation Job Number of Winning Bid Price Bidders (S in millions) Using Minitab, a simple linear regression model was fit. The partial output is atached. Using this output, answer questions (a), (b), and (c) below. Regression Analysis: Price versus Bidders Analysis of Variance or Ady ss Adj NSP-Value Douree Error Total Model Summary 5.000 7 30.0000 Coefficients Coef SE Coef 7-Value Term Conatant 8.750 0.779 Bidders -0.7500.14 Regression Equation Price r Regression Analysis: Price versus Bidders

Explanation / Answer

(a)

The estimated regression equation is,
Price = 8.75 - 0.75 * Bidders

(b)
Let n be the number of observations and k be the number of coefficients in the regression equation including intercept.
Then n = 8, k = 2

Degree of freedom of Total = n - 1 = 8 - 1 = 7
Degree of freedom of Error = n - k = 8 - 2 = 6
Degree of freedom of regression = k - 1 = 2 - 1 = 1

Adj SS for Regression = Adj SS for Total - Adj SS for Error = 30 - 5 = 25
Adj MS is calculated as,
Adj MS = Adj SS / DF

Adj MS for Regression = 25 / 1 = 25

Adj MS for Error = 5 / 6 = 0.8333

and F = Adj MS for Regression / Adj MS for Error = 25 / 0.8333 =

(c)

Numerator and Denominator DF for F -value are DF for regression and error respectively.

So, Numerator and Denominator DF for F -value are 1, 6

Critcal value of F for DF = 1, 6 is 5.99

As, the observed F-value (30.00) is greater than the critical value, the model is significant.

(d)

Coefficient of Determination = Adj SS for Regression / Adj SS for Total = 25 / 30 = 0.8333

Source DF Adj SS Adj MS F-value Regression 1 25 25 30.00 Error 6 5 0.8333 Total 7 30

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