Question

he 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^=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 33 34 45 48

Number of Bids 2 3 4 5 7

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

2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

3 of 6: Find the estimated value of y when x=34x=34. Round your answer to three decimal places.

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

5 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆy^ is given by?

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

Answer 1

Y	x	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
2 3 4 5 7	25 33 34 45 48	144.000 16.000 9.000 64.000 121.000 Sum: 354.000	4.840 1.440 0.040 0.640 7.840 Sum: 14.800	26.400 4.800 0.600 6.400 30.800 Sum: 69.000

The correlation coefficient

X Values
∑ = 185
Mean = 37
∑(X - Mx)2 = SSx = 354

Y Values
∑ = 21
Mean = 4.2
∑(Y - My)2 = SSy = 14.8

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 69

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 69 / √((354)(14.8)) = 0.9533

Testing of correlation that significant or not