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+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 0.5 1 2.5 3 4 5 5.5 Overall Grades 98 95 90 79 75 69 66 Table Step 6 of 6 : Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer #1

Step: 6

We have to find the value of the coefficient of determination.

The coefficient of determination is square of the sample correlation coefficient (r).

The formula of the sample correlation coefficient (r) is

n = 7

x | y | xy | x^2 | y^2 | |

0.5 | 98 | 49 | 0.25 | 9604 | |

1 | 95 | 95 | 1 | 9025 | |

2.5 | 90 | 225 | 6.25 | 8100 | |

3 | 79 | 237 | 9 | 6241 | |

4 | 75 | 300 | 16 | 5625 | |

5 | 69 | 345 | 25 | 4761 | |

5.5 | 66 | 363 | 30.25 | 4356 | |

Total | 21.5 | 572 | 1614 | 87.75 | 47712 |

r = - 0.9836

The coefficient of determination = R^2 = r^2 = ( - 0.9836)^2 =
**0.967**

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...

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...

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+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...

he 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...

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...

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, y ˆ = b 0 + b 1 x y^=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...

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+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...

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, y ˆ =b 0 +b 1 x y^=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...

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