The number of household members (X) and the amount spent on groceries (in $) per week (Y) are measured for six households in a local area in New York City. The data are given in the table below.

X | Y | X^{2} | Y^{2} | XY | |

2 | 90 | ||||

3 | 120 | ||||

5 | 175 | ||||

4 | 125 | ||||

1 | 35 | ||||

8 | 220 | ||||

Total | a | b | c | d | e |

Complete the above table in a sheet of paper and answer the following:

Remark: Round your answers to 2 decimal places

The value of a is Blank 1

The value of b is Blank 2

The value of c is Blank 3

The value of d is Blank 4

The value of e is Blank 5

What is the value of SS(X)?

The answer: Blank 6

What is the value of SS(Y)? =

The answer: Blank 7

What is the value of SS(XY)?

The answer. Blank 8

What is the value of the coefficient of linear correlation (r)?

The answer: Blank 9

## Solution

Blank 1 : **23**

Blank 2: **765**

Blank 3: **119**

Blank 4: **118,375**

Blank 5: **3,710**

Blank 6: **30.83**

Blank 7: **20,837.50**

Blank 8: **777.50**

Blank 9: **0.97**

## Calculations

X | Y | X^{2} | Y^{2} | XY | |

2 | 90 | 4 | 8100 | 180 | |

3 | 120 | 9 | 14400 | 360 | |

5 | 175 | 25 | 30625 | 875 | |

4 | 125 | 16 | 15625 | 500 | |

1 | 35 | 1 | 1225 | 35 | |

8 | 220 | 64 | 48400 | 1760 | |

Total | 23 | 765 | 119 | 118375 | 3710 |

a | b | c | d | e |

Key:

*X*: X Values*Y*: Y Values*M** _{x}*: Mean of X Values

*M*

*: Mean of Y Values*

_{y}*X – M*

_{x}&

*Y – M*

*: Deviation scores*

_{y}*(X – M*

_{x})

^{2}&

*(Y – M*

_{y}

*)*: Deviation Squared

^{2}*(X – M*

_{x}

*)(Y – M*

_{y}): Product of Deviation Scores

X – M_{x} | Y – M | (X – M_{x})^{2} | (Y – M_{y})^{2} | (X – M_{x})(Y – M_{y}) |

-1.83 | -37.5 | 3.36 | 1406.25 | 68.8 |

-0.83 | -7.5 | 0.69 | 56.25 | 6.3 |

1.17 | 47.5 | 1.36 | 2256.25 | 55.4 |

0.17 | -2.5 | 0.03 | 6.25 | -0.4 |

-2.83 | -92.5 | 8.03 | 8556.25 | 262.1 |

4.17 | 92.5 | 17.36 | 8556.25 | 385.4 |

SS(X) | SS(Y) | SS(XY) | ||

Mx: 3.83 | My: 127.50 | Sum: 30.83 | Sum: 20837.50 | Sum: 777.50 |

*X Values*

∑ = 23

Mean = 3.833

∑(X – M_{x})^{2} = SS_{x} = 30.833

*Y Values*

∑ = 765

Mean = 127.5

∑(Y – M_{y})^{2} = SS_{y} = 20837.5

*X and Y Combined**N* = 6

∑(X – M_{x})(Y – M_{y}) = 777.5

*R Calculation*

r = ∑((X – M_{y})(Y – M_{x})) / √((SS_{x})(SS_{y}))

r (blank 9)= 777.5 / √((30.833)(20837.5)) = **0.97 **

**By considering the value of the linear correlation coefficient (r) that you have calculated for the question “The number of household members (X) and the amount spent on groceries (in $) per week (Y) are measured for six households in a local area in New York City.”****The variables (X) and (Y) have a_**

## Answer:

High positive linear correlation

**Explanation:**

as r = 0.97

Which means the number of amount spent on groceries (in$) increase as the number of household members (X) increases.

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