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 31 32 34 38 48 Number of Bids 2 4 5 7 10

Step 3 of 6 : Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.

4.Determine the value of the coefficient of determination

5.Determine if the statement True or False."Not the points predicted by the linear model found on the same line.True or false

6.Determine the value of the dependent variable y at x=0 =

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 = -9.9435146 + 0.42468619 Price
Sample size: 5
R (correlation coefficient) = 0.96281005
R-sq = 0.92700319
Estimate of error standard deviation: 0.95139918

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-9.9435146	2.5539472	≠ 0	3	-3.8933908	0.0301
Slope	0.42468619	0.068804814	≠ 0	3	6.1723325	0.0086

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	34.484519	34.484519	38.097689	0.0086
Error	3	2.7154812	0.90516039
Total	4	37.2

Hence,

Step - 3: Change in dependent variable for a unit change in independent variable

= Slope

= 0.425

Step - 4: Coefficient of determination = 0.927

Step - 5: False

Step - 6: Value of dependent variable at x = 0 = y - intercept = -9.944