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   Number of Bids
30   2
32   4
43   5
45   6
50   7

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^.

Step 4 of 6:

Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6:

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

Step 6 of 6:

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

Answer 1

Solution:

here from the gievn data we solave this problem using the mintab statistical software as below

here corelation is

correlation of Price and Bids = 0.949 which is statistical significant

now

step 1:-

4.257 is the estimated slope.

step 2:-

19.570 is the estimated y-intercept

step 3:-

regression equation

Price = 19.57 + 4.257 Bids

According to this model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y^ is 4.257

step 5: -

value of the dependent variable y^ at x=0.

Price = 19.57 + 4.257 * 0

Price = 19.57

step 6:-

now the value of the coefficient of determination.

is R2   = 0.8999 = 89.99 %

Thank You..!!

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