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 25 27 28 30 45

Number of Bids 1 4 6 8 9

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 = 34. Round your answer to three decimal places.

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

Step 5 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 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

	Price in Dollars (X)	Number of Bids (Y)	X * Y	X2	Y2
	25	1	25	625	1
	27	4	108	729	16
	28	6	168	784	36
	30	8	240	900	64
	45	9	405	2025	81
Total	155	28	946	5063	198

Equation of regression line is Ŷ = a + bX


b = 0.302
a =( Σ Y - ( b * Σ X) ) / n
a =( 28 - ( 0.3023 * 155 ) ) / 5
a = -3.772
Equation of regression line becomes Ŷ = -3.772 + 0.302 X

Step 1

Slope    b = 0.302

Step 2

Y intercept a = -3.772

Step 3

When X = 34
Ŷ = -3.772 + 0.302 X
Ŷ = -3.772 + ( 0.302 * 34 )
Ŷ = 6.496

Step 4

When X = 0
Ŷ = -3.772 + 0.302 X
Ŷ = -3.772 + ( 0.302 * 0 )
Ŷ = -3.772

Step 5

When X = 1
Ŷ = -3.772 + 0.302 X
Ŷ = -3.772 + ( 0.302 * 1 )
Ŷ = -3.470

Step 6

r = 0.757

Coefficient of Determination
R² = r² = 0.572