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	21	22	35	38	44
Number of Bids	1	2	4	7	8

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: Determine the value of the dependent variable yˆ at x=0 ( b0, b1, x, y)

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

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

Step 1:

Sum of X = 160
Sum of Y = 22
Mean X = 32
Mean Y = 4.4
Sum of squares (SS_X) = 410
Sum of products (SP) = 119

Regression Equation = ŷ = bX + a

b 1= SP/SS_X = 119/410 = 0.290

Step 2: b0 = M_Y - bM_X = 4.4 - (0.29*32) = -4.888

ŷ = 0.290X - 4.888

Step 3: For X=0, ŷ=-4.888

Step 4:

So answer is False

Step 5: If the value of the independent variable is increased by one unit, then the change in the dependent variable yˆ is slope which is b1=0.290

Step 6:

X Values
∑ = 160
Mean = 32
∑(X - M_x)² = SS_x = 410

Y Values
∑ = 22
Mean = 4.4
∑(Y - M_y)² = SS_y = 37.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 119

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

r = 119 / √((410)(37.2)) = 0.964

So coefficient of determination is