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, y = bo + bix, 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 Number of Bids 149 11 165 15 167 16 177 18 195 19

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.
Step 3 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
Step 4 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.
Step 5 of 6: Find the estimated value of y when x=177. Round your answer to three decimal places.
Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable:y Independent Variable: x y=-13.882497 +0.17398884x Sample size: 5 R (correlation coefficient) = 0.94607399 R-sq=0.895056 Estimate of error standard deviation: 1.1650218 Parameter estimates: Parameter Estimate Std. Err. Intercept -13.882497 5.8911303 Slope 0.17398884 0.034396517 Alternative DF 0 3 0 3 T-Stat -2.3565081 5.0583274 P-value 0.0997 0.0149 Analysis of variance table for regression model: Source DF SS M S F-stat Model 1 34.728173 34.728173 25.586676 Error 3 4.0718271 1.3572757 Total 4 38.8 P-value 0.0149 Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 177 16.913529 0.56561095 (15.113502. 18.713555) (12.792056, 21.035001)

Step - 1) Slope = 0.174

Step - 2) Y-intercept = -13.882

Step - 3) False

Step - 4) the change in the dependent variable ˆy is = slope = 0.174

Step - 5)  estimated value = 16.914

Step - 6) the coefficient of determination = 0.895