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 31 39 40 46 48 Number of Bids 2 3 5 6 7 Table

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=46x=46. Round your answer to three decimal places.

Step 4 of 6:

Determine the value of the dependent variable yˆy^ at x=0x=0.

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

Step 1: Sum of X = 204
Sum of Y = 23
Mean X = 40.8
Mean Y = 4.6
Sum of squares (SS_X) = 178.8
Sum of products (SP) = 52.6

Regression Equation = ŷ = bX + a

b = SP/SS_X = 52.6/178.8 = 0.294

Step 2: a = M_Y - bM_X = 4.6 - (0.29*40.8) = -7.403

Step 3: using 1 and 2 we get

ŷ = 0.294X - 7.403

For x=46,

ŷ = (0.294*46) - 7.403=6.121

Step 4: For x=0, ŷ = 0.294*0 - 7.403=-7.403

Step 5:

So answer is True

Step 6:

X Values
∑ = 204
Mean = 40.8
∑(X - M_x)² = SS_x = 178.8

Y Values
∑ = 23
Mean = 4.6
∑(Y - M_y)² = SS_y = 17.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 52.6

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 52.6 / √((178.8)(17.2)) = 0.949

So r^2=0.901