Bank
Kentucky Derby. On the first Saturday in May, the granddaddy of horse race – the Kentucky Derby is run at Churchill Downs in Louisville, Kentucky Derby. The amount of money bet, in millions of dollars, on this race for the file named DERBY5 on the CD. Build an extrapolative model for the amount bet and provide a justification for the model. Use linear and/or nonlinear trends to build the model. Once you have chosen your preferred model, use it to forecast the amount bet in 1993 and 1994.
May not be linear. As the number of date increases, the number of bets also increases. But the rate of increase begins to slow over time, thus resulting in a pattern that may be better modeled by curve than a straight line.
The plot of y versus x has been reproduced with a curve drawn in that approximates the relationship between the two variables.
POLYNOMIAL REGRESSION
Regression Results for Kentucky Derby Example Using Only Date as an Explanation Variable.
Regression Results for Kentucky Derby Example with Second-Order Term Added.
The primary check that should be made as this point to determine whether the second-order model is preferred to the original linear model is not test whether the coefficient of the second-order term is significantly different from zero. To determine whether the x2 variable has significantly improved the fit of the regression, the following hypotheses can be tested:
H0 : β2 = 0
H0 : β2 ≠ 0
Where β2 is the coefficient of x2 . The t test discussed in Chapter 4 can be used to conduct the test. For α=0.05, the decision rule is
Reject H0 if t > 2.11 or t < -2.11 , Do not reject H0 if -2.11 or < =t <= -2.11
This statistic value is t = -10.91. The null hypotheses is rejected. The x2 term adds significantly to the ability of the regression to explain the variation in y. Thus, the term should remain in the equation. Note that the p value could also have been used to conduct this (p value = 0.000 < 0.005,
May not be linear. As the number of date increases, the number of bets also increases. But the rate of increase begins to slow over time, thus resulting in a pattern that may be better modeled by curve than a straight line.
The plot of y versus x has been reproduced with a curve drawn in that approximates the relationship between the two variables.
POLYNOMIAL REGRESSION
Regression Results for Kentucky Derby Example Using Only Date as an Explanation Variable.
Regression Results for Kentucky Derby Example with Second-Order Term Added.
The primary check that should be made as this point to determine whether the second-order model is preferred to the original linear model is not test whether the coefficient of the second-order term is significantly different from zero. To determine whether the x2 variable has significantly improved the fit of the regression, the following hypotheses can be tested:
H0 : β2 = 0
H0 : β2 ≠ 0
Where β2 is the coefficient of x2 . The t test discussed in Chapter 4 can be used to conduct the test. For α=0.05, the decision rule is
Reject H0 if t > 2.11 or t < -2.11 , Do not reject H0 if -2.11 or < =t <= -2.11
This statistic value is t = -10.91. The null hypotheses is rejected. The x2 term adds significantly to the ability of the regression to explain the variation in y. Thus, the term should remain in the equation. Note that the p value could also have been used to conduct this (p value = 0.000 < 0.005,