Question

sales of body price of lens gender sales of lens

155 700 1 122

101 650 1 120

157 725 0 135

180 575 1 95

150 600 0 100

201 750 0 174

99 560 1 118

137 500 0 130

155 675 1 128

165 550 1 166

152 725 0 131

127 750 1 102

217 565 0 165

186 670 0 154   

176 600 1 97

123 585 0 129

109 645 0 98

90 575 1 105

176 660 0 120

129 650 1 105

1. Find a 99% confidence interval for the mean sales of the lens when sales of the camera body are 150 and the price of the lens is $700 using PH stat in excel.  Provide an explanation of the meaning of this interval.

2. Find a 99% prediction interval for the sales of the lens when sales of the camera body are 150 and the price of the lens is $700 using PH stat in excel. Explain its meaning relative to the problem. Compare the width of this interval to that of the interval calculated in the previous part of the problem. Give a reason for any difference in the width of this interval and the one you found in the previous part of the problem.

3. Find the sample coefficient of determination for the data using PH stat in excel. Explain its meaning in the context of the problem.

Answer 1

Question 1:

The 99% confidence interval for the mean sales of the lens when sales of the camera body are 150 and the price of the lens is $700 is between 106.224 and 144.009.

We are 99% confident that the true mean sales of the lens when sales of the camera body are 150 and the price of the lens is $700 is between 106.224 and 144.009.

Question 2:

The 99% prediction interval for the mean sales of the lens when sales of the camera body are 150 and the price of the lens is $700 is between 60.233 and 189.999.

We are 99% confident that the true mean sales of the lens when sales of the camera body are 150 and the price of the lens is $700 for a future value is between 60.233 and 189.999.

The prediction interval is wider than the confidence interval.

Question 3:

R2 = 0.303

30.3% of the variation in the model is explained.

	R²	0.303
	Adjusted R²	0.221
	R	0.550
	Std. Error	21.417
	n	20
	k	2
	Dep. Var.	sales of lens
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,384.3893	2	1,692.1946	3.69	.0467
Residual	7,797.8107	17	458.6947
Total	11,182.2000	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=17)	p-value	99% lower	99% upper
Intercept	66.3946
sales of body	0.3821	0.1424	2.684	.0157	-0.0305	0.7947
price of lens	0.0020	0.0688	0.029	.9770	-0.1973	0.2014
Predicted values for: sales of lens
			99% Confidence Interval	99% Prediction Interval
sales of body	price of lens	Predicted	lower	upper	lower	upper
150	700	125.116	106.224	144.009	60.233	189.999