Question

The following data was collected during a study to determine if there is a relationship between the vertical drop of the mountain and the number of trails at the resort in New York State. (1200, 30), (700, 50), (700, 24), (1500, 62), (1010, 23), (3350, 67), (400, 15), (1600, 34) a.) Generate the regression equation. b.) Determine the correlation coefficient. c.) Is there enough evidence to conclude that the slope of the regression line is not zero at the 98% confidence level? Explain. d.) A ski resort in Colorado, Aspen Highlands, has a vertical drop of 3635’. Give two reasons why the model created in this problem cannot be used to make a prediction for the number of trails at Aspen Highlands.

Answer 1

(a)

x = Vertical drop, y = Number of trails

Regression Analysis
	r²	0.526	n	8
	r	0.725	k	1
	Std. Error	14.307	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,362.7358	1	1,362.7358	6.66	.0418
Residual	1,228.1392	6	204.6899
Total	2,590.8750	7
Regression output					confidence interval
variables	coefficients	std. error	t (df=6)	p-value	98% lower	98% upper	std. coeff.
Intercept	18.3478						0.000
x	0.0151	0.0059	2.580	.0418	-0.0033	0.0335	0.725

The regression equation is y = 18.3478 + 0.0151x

(b) r = 0.725

(c) p- value (0.0418) > 0.02, hence the regression is not significant

(d) (i) This model is only for resorts in the New York state, and so can't be used for Colorado state (ii) r^2 value is low for the model, so predictions based on this model may not be reliable.