Question

Each month, the owner of a restaurant records y=monthly sales
receipts and x=amount spent that month on advertising, both in
thousands of dollars. For the first four months of operation, the
observations are as shown in the table.

Advertising Sales

0 4

1 7

3 9

5 11

a.Find the mean and standard deviation for each variable.

b.Find the values for a and b in the regression line.

c. Find the correlation coefficient. Interpret the relationship
between two variables using correlation coefficient.

Answer #1

n= | 4.0000 | |

X̅=ΣX/n | 2.250 | |

Y̅=ΣY/n | 7.750 | |

s_{x}=(√(Σx^{2}-(Σx)^{2}/n)/(n-1))= |
2.2174 | |

s_{y}=(√(Σy^{2}-(Σy)^{2}/n)/(n-1))= |
2.9861 | |

Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)= | 6.4167 | |

r=Cov/(Sx*Sy)= | 0.9691 |

a)

mean of advertisement =2.25

standard deviation of advertisement =2.2174

mean of Sales =7.75

standard deviation of Sales =2.9861

b)

slope= b = |
r*S_{y}/S_{x}=1.3051 |
||

intercept=
a _{ } = |
(Σy-β_{1}Σx)/n=4.8136 |

c)

correlation coefficient r=0.9691

since correlation coefficient is positive and near 1 , there apears a strong positive linear relation between advertisement and sales

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
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From the April 2004 Issue
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