Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on her age. 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.

Age | 3535 | 4343 | 5353 | 5454 | 5555 |
---|---|---|---|---|---|

Bone Density | 350350 | 340340 | 339339 | 321321 | 310310 |

Table

Copy Data

Step 6 of 6 :

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

Answer #1

**Solution :**

X | Y | XY | X^2 | Y^2 |

35 | 350 | 12250 | 1225 | 122500 |

43 | 340 | 14620 | 1849 | 115600 |

53 | 339 | 17967 | 2809 | 114921 |

54 | 321 | 17334 | 2916 | 103041 |

55 | 310 | 17050 | 3025 | 96100 |

n | 5 |

sum(XY) | 79221.00 |

sum(X) | 240.00 |

sum(Y) | 1660.00 |

sum(X^2) | 11824.00 |

sum(Y^2) | 552162.00 |

Numerator | -2295.00 |

Denominator | 2814.11 |

r | -0.8155 |

r square | 0.6651 |

The coefficient of determination,

r2 = 0.665

**Answer :**

**The value of the coefficient of determination is
0.665**

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
4343
4949...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
4646
4848...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
5050
5959...

The table below gives
the age and bone density for five randomly selected women. Using
this data, consider the equation of the regression line,
yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone density based on
her age. 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.
Age
35
42...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
46
48...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
46
48...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
46
48...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1x, for predicting a woman's bone density
based on her age. 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. Age 50 59...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age
39
47...

The table below gives the age and bone density for five randomly
selected women. Using this data, consider the equation of the
regression line, yˆ=b0+b1xy^=b0+b1x, for predicting a woman's bone
density based on her age. 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.
Age Bone Density...

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