Question

The Insurance Institute for Highway Safety develops ratings for collision claims and comprehensive claims (higher numbers reflect higher claim rates) by type of vehicle. To evaluate if a relationship exists between collision and comprehensive claim rates for midsize four-door cars, an insurance agent takes a sample of 12 vehicles in this category. The data appears in the Insurance worksheet of the Simple Regression worksheet below.    

a) Draw a scatter plot of the data. Does there appear to be a linear association between collision and comprehensive claim rates?  

b) Use JMP to find a confidence interval on the sample correlation coefficient between collision and comprehensive claim rates. Are the variables significantly correlated at alpha = 0.05?

c) Fit the simple linear regression model using comprehensive claim rates as the dependent or Y variable and collision claim rates the dependent or X variable. Is the model significant at alpha= 0.05?

d) Provide the equation of the fit line. Interpret the parameter estimates in the context of the problem.

e) Use a hypothesis test to determine if an increase in 1 collision claim rate corresponds to an increase in comprehensive claim rates different than 1, i.e., test the hypothesis H0: Beta1 = 1 versus H1: Beta 1 is not equal to 1 using alpha of 0.05.

f) Provide a point prediction and a 95% prediction interval for the comprehensive claim rate for a vehicle with a collision claim rate of 100.

Collision	Comprehensive
113	89
108	91
90	74
124	92
131	108
126	108
93	79
105	97
106	86
99	71
116	98
120	93

Answer 1

a) Draw a scatter plot of the data. Does there appear to be a linear association between collision and comprehensive claim rates?  

Yes, there is a positive correlation between the two variables.

b) Use JMP to find a confidence interval on the sample correlation coefficient between collision and comprehensive claim rates. Are the variables significantly correlated at alpha = 0.05?

The P-Value is .000332. The result is significant at p < .05.

c) Fit the simple linear regression model using comprehensive claim rates as the dependent or Y variable and collision claim rates the dependent or X variable. Is the model significant at alpha= 0.05?

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.860144398
R Square	0.739848385
Adjusted R Square	0.713833224
Standard Error	6.302789191
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1129.748484	1129.748484	28.43912331	0.000331617
Residual	10	397.2515158	39.72515158
Total	11	1527
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4.584377075	16.21310094	0.282757573	0.783129147	-31.54066289	40.70941704
Collision	0.77459615	0.145250365	5.332834453	0.000331617	0.45095817	1.098234129

Significance F < 0.05, which means the model is significant.

d) Provide the equation of the fit line. Interpret the parameter estimates in the context of the problem.

The model suggests that an increase in 1 collision claim rate corresponds to a value of 0.77 increase in the comprehensive claim and a fixed cost =4.584.