Question

The table below gives the number of absences and the overall grade in the class for seven randomly selected students. Based on this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for using the number of absences to predict a student's overall grade in the class. 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.

Number of Absences	00	11	22	33	66	77	88
Grade	3.93.9	3.53.5	3.13.1	2.72.7	2.32.3	2.22.2	1.91.9

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 yˆy^.

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:

Find the estimated value of y when x=2x=2. Round your answer to three decimal places.

Step 6 of 6:

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

Table

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Step 1 of 6:

Find the estimated slope. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is :

Step - 1) Slope = -0.228

Step - 2) Y-intercept = 3.678

Step - 3)  the change in the dependent variable ˆy is = slope = -0.228

Step - 4) False

Step - 5)  estimated value = 3.223

Step - 6) the coefficient of determination = 0.947