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: 22 23 35 38 49 Number of Bids 3 4 5 6 8

1. Find the estimated slope. Round your answer to three decimal places. 2. Find the value of the coefficient of determination. Round your answer to three decimal places. 3.Find the estimated y-intercept. Round your answer to three decimal places 4.Determine the value of the de[endent variable of ^y at x=0 5.According to the equation of the regression line, if the independent variable is increased by one unit what is the change in the dependent variable y? 6.Not all points predicted by the linear model fall on the same line True or False

Answer 1

1.

Sum of X = 167
Sum of Y = 26
Mean X = 33.4
Mean Y = 5.2
Sum of squares (SSX) = 505.2
Sum of products (SP) = 84.6

Regression Equation = ŷ = bX + a

b = SP/SSX = 84.6/505.2 = 0.167

2.

X Values
∑ = 167
Mean = 33.4
∑(X - Mx)2 = SSx = 505.2

Y Values
∑ = 26
Mean = 5.2
∑(Y - My)2 = SSy = 14.8

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 84.6

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

r = 84.6 / √((505.2)(14.8)) = 0.978

So r^2=0.978^2=0.956

3. a = MY - bMX = 5.2 - (0.17*33.4) = -0.393

4. ŷ = 0.167X - 0.393

For x=0.5, ŷ = 0.167*0.5 - 0.393=-0.3095

5. If the independent variable is increased by one unit what is the change in the dependent variable y will increase by 0.167

6.

So answer is True