Question

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 23 25 32 36 40 Number of Bids 2 4 5 8 10 Table Step 4 of 6: Find the estimated value of y when x=23. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Number of Bids
Independent Variable: Price
Number of Bids = -7.6576402 + 0.43133462 Price
Sample size: 5
R (correlation coefficient) = 0.97109005
R-sq = 0.94301589
Estimate of error standard deviation: 0.88033169

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-7.6576402	1.9501198	≠ 0	3	-3.9267537	0.0294
Slope	0.43133462	0.061216863	≠ 0	3	7.04601	0.0059

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	38.475048	38.475048	49.646256	0.0059
Error	3	2.3249516	0.77498388
Total	4	40.8

Predicted values:

X value	Pred. Y	s.e.(Pred. y)	95% C.I. for mean	95% P.I. for new
23	2.2630561	0.63794903	(0.23281756, 4.2932946)	(-1.1968395, 5.7229517)

Since p - value is 0.0059 which is less. The correlation is significant. Hence,

For x = 23: y = 2.263