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 24 26 33 45

Number of Bids 3 6 7 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 X	Bids Y	X * Y
	23	3	69	529	9
	24	6	144	576	36
	26	7	182	676	49
	33	8	264	1089	64
	45	9	405	2025	81
Total	151	33	1064	4895	239

Equation of regression line is


b = 0.201

a =( 33 - ( 0.2013 * 151 ) ) / 5
a = 0.52
Equation of regression line becomes

Slope b = 0.201

Intercept a = 0.520

When X = 34
= 0.52 + 0.201 X
= 0.52 + 0.201 * 34
= 7.354

Step 4

When Y = 0

Step 5

If X changes by 1 unit, then Y changes by 0.201.

r = 0.8

Coefficient of Determination

Explained variation = 0.64* 100 = 64%
Unexplained variation = 1 - 0.64* 100 = 36%