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

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=49. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable y^ at x=0. ( b0, b1, x or y)

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 y^.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

step 1:

here we need to find the estimated slope, that is we need to find b1

the equation is given as y = b0 + b1*x

the data is given as

Price in dollars (X)	22	23	35	38	49
Number of Bids (Y)	3	4	5	6	8

to find b1 we need to solve the below two equations simultaneously

            ............(A)

            ............(B)

so here n = 5

substituting the values in equation A and B we get,

26 = b0*5 + b1*167                .......(a)

953 = b0*167 + b1*6083       ..........(b)

now from equation (a) we get,

substituting this value in equation (b), we get

thus the estimated slope is 0.167.

Step 2:

to find the estimated y-intercept, that is we need to find b0

fom step 1, substituting the value of b1 in equation (a), we get

26 = b0*5 + b1*167                .......(a)

hence the y-intercept is -0.393.

Step 3:

now the equation is y^ = -0.393 + 0.167*x

now put x=49 in the above equation, we get

y^ = -0.393 + 0.167*49

y^ = -0.393 + 8.183

y^ = 7.79

Step 4:

again put x=0 in the step 3 equation, we get

y^ = -0.393 + 0.167*0

y^ = -0.393 + 0

y^ = -0.393

Step 5:

here the estimated linear model is given as

y^ = -0.393 + 0.167*x

now here we have to find y^ when x=x+1

so,

y^ = -0.393 + 0.167*(x+1)

y^ = -0.393 + 0.167*x + 0.167*1

y^ = 0.167 - 0.393 +0.167*x

y^ = -0.226 +0.167*x

Step 6:

to find Coefficient of determination  

now,

so,

Similarly,

so,  

now,

so,

hence,

therefore the coeficient of determination is 0.978.

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Thank You :)