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	27	28	29	34	38
Number of Bids	2	3	5	6	10

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: 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 y^ (y hat).

Step 4 of 6: Determine the value of the dependent variable y^ at x = 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 = 156
Sum of Y = 26
Mean X = 31.2
Mean Y = 5.2
Sum of squares (SSX) = 86.8
Sum of products (SP) = 55.8

Regression Equation = ŷ = bX + a

b = SP/SSX = 55.8/86.8 = 0.643

Step 2: a = MY - bMX = 5.2 - (0.64*31.2) = -14.857

Step 3: ŷ = 0.643X - 14.857

As slope value is 0.643

If the value of the independent variable is increased by one unit, then 0.643 change in the dependent variable y^

Step 4: For x=0, it would be y intercept and its value is -14.857

Step 5:

As we see that not all points lie on the line.

So Not all points predicted by the linear model fall on the same line" is true.

Step 6:

X Values
∑ = 156
Mean = 31.2
∑(X - Mx)2 = SSx = 86.8

Y Values
∑ = 26
Mean = 5.2
∑(Y - My)2 = SSy = 38.8

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 55.8

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

r = 55.8 / √((86.8)(38.8)) = 0.962

So r^2=coefficient of determination=0.962^2=0.925