Question

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. 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.

Hours Unsupervised	0	0.5	1.5	2.5	4	4.5	6
Overall Grades	88	79	76	72	65	63	62

Table

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 5 of 6:

Determine if the statement "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

The equation of the regression line is

where , x - Hours unsupervised, y - overall grades

The formula to find the slope is,

By plugging the values in the formula of slope,

Estimated slope = -4.136

The formula of intercept is,

Estimated intercept = 83.369

The statement is false, because the predictions will fall on the same line but the actual values will may generally not.

Coefficient of determination

First find the coefficient of correlation

The formula is,

Coefficient of determination = 0.914