**Question 1 **

The regression equation is intended to be the “best fitting” straight line for a set of data. What is the criterion for “best fitting”?

The best fitting line is determined by the error between the predicted *Y* values on the line and the actual *Y* values in the data. The regression equation is determined by the line with the smallest total squared error.

**Question 2**

A set of n=15 pairs of scores (X and Y values) has a *SS*_{X }= 15 and *SP *= -60. If the mean for the X values is *M*_{X}= 6 and the mean for the Y values is* M*_{y}= 12, find the regression equation for predicting Y from the X values.

*b* = *SP/* *SS*_{X}

*b* = -60/15 = -4

*a* = *M*_{Y} – *bM*_{X}

*a* = 12 – (-4)(6) = 12 + 24 = 36

*Ŷ *= *bX* + *a*

*Ŷ *= -4X + 36

**Question 3**

A set of n =25 pairs of scores (X and Y values) produces a regression equation of* Ŷ *= 3X – 6. Find the predicted Y value for each of the following X scores:

- 0

*Ŷ *= 3(0) – 6 = -6

- 1

*Ŷ *= 3(1) – 6 = -3

- 3

*Ŷ *= 3(3) – 6 = 3

- -3

*Ŷ *= 3(-3) – 6 = -15

**Question 4**

**We have to find a and b: First we find b**

b = *SP/* *SS*_{X}

*SP* = ƩXY – ƩXƩY

n

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

- We find the numerator of
*b*: SP

X | Y | XY |

1 | 2 | 2 |

4 | 7 | 28 |

3 | 5 | 15 |

2 | 1 | 2 |

5 | 8 | 40 |

3 | 7 | 21 |

**ƩX = 18 ƩY = 30 ƩXY = 108**

*SP* = ƩXY – ƩXƩY

n

*SP* = 108 – (18)(30) = 108-90 = 18

6

- We find the denominator of
*b: SS*_{X}

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

*M*_{X}= ƩX/n = 18/6 =3

X | X – M_{X} |
(X – M_{X})^{2} |
Y |

1 | -2 | 4 | 2 |

4 | 1 | 1 | 7 |

3 | 0 | 0 | 5 |

2 | -1 | 1 | 1 |

5 | 2 | 4 | 8 |

3 | 0 | 0 | 7 |

* SS*

*SS** _{X} *= 10

- Calculate b

b = *SP/* *SS*_{X }

*b* = 18/10 = 1.8

**Now we find a**

*a* = *M*_{Y} – *bM*_{X}

*M*_{X}= ƩX/n = 18/6 =3

*M*_{Y}= ƩY/n = 30/6 =5

*a* = 5 – (1.8)(3) = 5- 5.4 = -0.4

**The linear regression equation for predicting Y from X is:**

*Ŷ *= *bX* + *a *

*Ŷ ***= 1.8X – 0.4 **

**Question 5**

**We have to find a and b: First we find b**

b = *SP/* *SS*_{X}

*SP* = ƩXY – ƩXƩY

n

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

- We find the numerator of
*b*: SP

X | Y | XY |

3 | 8 | 24 |

6 | 4 | 24 |

3 | 5 | 15 |

3 | 5 | 15 |

5 | 3 | 15 |

**ƩX = 20 ƩY = 25 ƩXY = 93**

*SP* = ƩXY – ƩXƩY

n

*SP* = 93 – (20)(25) = 93 -100 = -7

5

- We find the denominator of
*b: SS*_{X}

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

*M*_{X}= ƩX/n = 20/5 =4

X | X – M_{X} |
(X – M_{X})^{2} |
Y |

3 | -1 | 1 | 8 |

6 | 2 | 4 | 4 |

3 | -1 | 1 | 5 |

3 | -1 | 1 | 5 |

5 | 1 | 1 | 3 |

* SS*

* *

*SS** _{X} *= 8

- Calculate b

b = *SP/* *SS*_{X }

*b* = -7/8 = -.875

**Now we find a**

*a* = *M*_{Y} – *bM*_{X}

*M _{X}= ƩX/n = 20/5 =4*

*M*_{Y}= ƩY/n = 25/5 =5

*a* = *5* – (-.875)(4) = 5 + 3.5 = 8.5

**The linear regression equation for predicting Y from X is:**

*Ŷ *= *bX* + *a *

*Ŷ *= -.875*X* + 8.5

**Question 6**

- Use the data to find the regression equation for predicting memory scores from age

**We have to find a and b: First we find b**

b = *SP/* *SS*_{X}

*SP* = ƩXY – ƩXƩY

n

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

- We find the numerator of
*b*: SP

Age (X) | Memory Score (Y) | XY |

25 | 10 | 250 |

32 | 10 | 320 |

39 | 9 | 351 |

48 | 9 | 432 |

56 | 7 | 392 |

**ƩX = 200 ƩY = 45 ƩXY = 1745**

*SP* = ƩXY – ƩXƩY

n

*SP* = 1745 – (200)(45) = 1745- 1800 = -55

5

- We find the denominator of
*b: SS*_{X}

*SS*_{X} = Ʃ(X – *M*_{X})^{2}

*M*_{X}= ƩX/n = 200/5 =40

X | X – M_{X} |
(X – M_{X})^{2} |
Y |

25 | -15 | 225 | 10 |

32 | -8 | 64 | 10 |

39 | -1 | 1 | 9 |

48 | 8 | 64 | 9 |

56 | 16 | 256 | 7 |

* SS*

* *

*SS** _{X} *= 610

- Calculate b

b = *SP/* *SS*_{X }

*b* = –55/610 = -.09

** **

**Now we find a**

*a* = *M*_{Y} – *bM*_{X}

*M _{X}= ƩX/n = 200/5 =40*

*M*_{Y}= ƩY/n = 45/5 =9

*a* = *9* – (-.09)(40) = 9 + 3.6 = 12.6

**The linear regression equation for predicting Y from X is:**

*Ŷ *= *bX* + *a *

*Ŷ *= *-.09X* + 12.6

**Questions 7 to 9**

Use the regression equation you found in question 6 to find the predicted memory scores for the following ages: 28, 43, and 50

*Ŷ *= *-0.09(**28)* + 12.6 = 10.08

*Ŷ *= *-0.09(**43)* + 12.6 = 8.73

*Ŷ *= *-0.09(**50)* + 12.6 = 8.1

** **

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more