Question

6. 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 135 138 163 168 192

Number of Bids    11    12   15 17 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: Find the estimated value of y when x=163. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable yˆ at x=0.

b0, or b1, or x, or y.

Step 5 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

	Price (X)	Bids (Y)	X * Y	X2	Y2
	135	11	1485	18225	121
	138	12	1656	19044	144
	163	15	2445	26569	225
	168	17	2856	28224	289
	192	19	3648	36864	361
Total	796	74	12090	128926	1140

Step 1

b = ( 5 * 12090 - 796 * 74 ) / ( 5 * 128926 - ( 796 )²)
b = 0.140

Step 2

a =( Σ Y - ( b * Σ X) ) / n
a =( 74 - ( 0.1404 * 796 ) ) / 5
a = -7.546

Step 3

Equation of regression line becomes Ŷ = -7.5464 + 0.1404 X

When X = 163
Ŷ = -7.546 + 0.14 X
Ŷ = -7.546 + ( 0.14 * 163 )
Ŷ = 15.274

Step 4

Ŷ = -7.5464 + 0.1404 X

Ŷ = -7.5464 + 0.1404 ( 0 )

Ŷ = - 7.5464

Step 5

We can see that mostly all points are lying on the same line, hence we can say that statement is true.

Step 6

r = 0.984

Coefficient of Determination
R² = r² = 0.969