Question

Use Excel Analysis ToolPak to solve.

Helmet   Weight   Price
Pyrotect Pro Airflow    64   248
Pyrotect Pro Airflow Graphics   64   278
RCi Full Face    64   200
RaceQuip RidgeLine    64   200
HJC AR-10    58   300
HJC Si-12   47   700
HJC HX-10   49   900
Impact Racing Super Sport   59   340
Zamp FSA-1   66   199
Zamp RZ-2   58   299
Zamp RZ-2 Ferrari   58   299
Zamp RZ-3 Sport   52   479
Zamp RZ-3 Sport Painted   52   479
Bell M2    63   369
Bell M4    62   369
Bell M4 Pro   54   559
G Force Pro Force 1   63   250
G Force Pro Force 1 Grafx   63   280

Automobile racing, high-performance driving schools, and driver education programs run by automobile clubs continue to grow in popularity. All these activities require the participant to wear a helmet that is certified by the Snell Memorial Foundation, a not-for-profit organization dedicated to research, education, testing, and development of helmet safety standards. Snell “SA” (Sports Application) rated professional helmets are designed for auto racing and provide extreme impact resistance and high fire protection. One of the
key factors in selecting a helmet is weight, since lower weight helmets tend to place less stress on the neck. The following data show the weight and price for 18 SA helmets
(SoloRacer website, April 20, 2008).

Required:

a. Develop a scatter diagram with weight as the independent variable.
b. Does there appear to be any relationship between these two variables?
c. Develop the estimated regression equation that could be used to predict the price given the weight.
d. Test for the significance of the relationship (slope) at the .05 level of significance.
e. Did the estimated regression equation provide a good fit? Explain.

Answer 1

helmet	weight(X)	price(Y)	XY	(X^2)	(Y^2)
Pyrotect Pro Airflow	64	248	15872	4096	61504
Pyrotect Pro Airflow Graphics	64	278	17792	4096	77284
RCi Full Face	64	200	12800	4096	40000
RaceQuip RidgeLine	64	200	12800	4096	40000
HJC AR-10	58	300	17400	3364	90000
HJC Si-12	47	700	32900	2209	490000
HJC HX-10	49	900	44100	2401	810000
Impact Racing Super Spor	59	340	20060	3481	115600
Zamp FSA-1	66	199	13134	4356	39601
Zamp RZ-2	58	299	17342	3364	89401
Total	593	3664	204200	35559	1853390
Correlation = (it is strongly negatively correlated,becoz increase in weight decreases the price and they have inverse relationship among them) -0.921461091

Y(dependent variable) = a(intercept) + b(slope)X(independent variable) + e(error term)

Y = 232.8500253 + 1.859443038 * X

Regression Statistics
Multiple R	0.921461091
R Square	0.849090543
Adjusted R Square	0.830226861
Standard Error	98.17057993
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	433800.6979	433800.6979	45.01191948	0.000151282
Residual	8	77099.70211	9637.462763
Total	9	510900.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	2333.817813	294.8851541	7.914327936	4.71834E-05	1653.811428	3013.824197	1653.811428	3013.824197
weight(X)	-33.17736615	4.945134851	-6.709092299	0.000151282	-44.58086757	-21.77386473	-44.58086757	-21.77386473
RESIDUAL OUTPUT
Observation	Predicted price(Y)	Residuals	Standard Residuals
1	210.4663791	37.53362091	0.405522885
2	210.4663791	67.53362091	0.729650594
3	210.4663791	-10.46637909	-0.113081449
4	210.4663791	-10.46637909	-0.113081449
5	409.530576	-109.530576	-1.183396488
6	774.4816037	-74.48160365	-0.804718385
7	708.1268714	191.8731286	2.073046586
8	376.3532098	-36.35320985	-0.392769421
9	144.1116468	54.88835321	0.593027872
10	409.530576	-110.530576	-1.194200745

yes the regression model is a good fit