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 | 1.5 | 2.5 | 3 | 4.5 | 5 | 6 |

Overall Grades | 94 | 92 | 86 | 82 | 79 | 71 | 62 |

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=2.5. Round your answer to three decimal places.

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

Step 5 of 6: Find the error prediction when x=2.5. 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.

Answer #1

Ans:

1 | 2 | 3 | 4 | 5 | 6 | 7 | Total | |

Hours Unsupervised,x | 0 | 1.5 | 2.5 | 3 | 4.5 | 5 | 6 | 22.5 |

Overall Grades,y | 94 | 92 | 86 | 82 | 79 | 71 | 62 | 566 |

xy | 0 | 138 | 215 | 246 | 355.5 | 355 | 372 | 1681.5 |

x^2 | 0 | 2.25 | 6.25 | 9 | 20.25 | 25 | 36 | 98.75 |

y^2 | 8836 | 8464 | 7396 | 6724 | 6241 | 5041 | 3844 | 46546 |

1)

slope,b1=(7*1681.5-22.5*566)/(7*98.75-22.5^2)=**-5.214**

2)

intercept,b0=(566-(-5.21351)*22.5)/7=**97.615**

3)

Regression equation:

y'=97.615-5.214 x

**when x=2.5**

y'=97.615-5.214*2.5=**84.580**

4)

when x=0

y'=97.615-5.214*0

y'=97.615

5)

observed value of y when x=2.5 is 86

Error=86-84.580=**1.420**

6)

r=(7*1681.5-22.5*566)/SQRT((7*98.75-22.5^2)*(7*46546-566^2))=-0.9159

coefficient of
determination,R^2=(-0.9159)^2=**0.920**

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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...

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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...

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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
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significant for...

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...

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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
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