Question

1. An accountant for a large department store has the business
objective of developing a model to predict the amount of time it
takes to process invoices. Data are collected from the past 32
working days, and the number of invoices processed and completion
time (in hours) are stored (**invoice.xlsx**).

(a) At the level ? = 0.01, conduct a *t* test with the
null hypothesis of zero correlation between the number of invoices
and the completion time.

(b) Using the least-squares method, determine the regression coefficients ?0 and ?1 in the linear regression model with the number of invoices as an independent variable and the completion time as a dependent variable

(c) At the level ? = 0.01, is there evidence of a linear effect
of the number of invoices on the completion time? Answer based on
the *F* test in ANOVA analysis

(d) Determine the coefficient of determination, ?2, and
interpret its meaning (e) Determine the standard error of estimate,
and interpret its meaning

(f) At the level ? = 0.01, conduct a *t* test about the
population slope ?1

(g) At the 99% confidence level, obtain the confidence interval of
?1

(h) Predict the expected completion time when the number of
invoices is 100.

(i) Evaluate the assumptions of linearity and equal variance by
constructing a residual plot with

? and ? axis for the number of invoices and the residual,
respectively

(j) Evaluate the assumption of independence, particularly about
autocorrelation, by constructing

a residual plot with ? and ? axis for the order of observations and the residual, respectively (k) Evaluate the assumption of normality by constructing a normal probability plot with ? and

? axis for the quantile and the residual, respectively

Invoices | Time |

103 | 1.5 |

173 | 2.0 |

149 | 2.1 |

193 | 2.5 |

169 | 2.5 |

29 | 0.5 |

188 | 2.3 |

19 | 0.3 |

201 | 2.7 |

58 | 1.0 |

110 | 1.5 |

83 | 1.2 |

60 | 0.8 |

25 | 0.4 |

60 | 1.8 |

190 | 2.9 |

233 | 3.4 |

289 | 4.1 |

45 | 1.2 |

70 | 1.8 |

241 | 3.8 |

163 | 2.8 |

120 | 2.5 |

201 | 3.3 |

135 | 2.0 |

80 | 1.7 |

77 | 1.7 |

222 | 3.1 |

181 | 2.8 |

30 | 1.0 |

61 | 1.9 |

120 | 2.6 |

Answer #1

Sol:

install analysis tool pack in excel.

then go to

Data >Data analysis >Regression

you will get

SUMMARY OUTPUT | ||||||

Regression Statistics | ||||||

Multiple R | 0.928597392 | |||||

R Square | 0.862293116 | |||||

Adjusted R Square | 0.857702886 | |||||

Standard Error | 0.3673572 | |||||

Observations | 32 | |||||

ANOVA | ||||||

df | SS | MS | F | Significance F | ||

Regression | 1 | 25.35114813 | 25.35115 | 187.854 | 1.87986E-14 | |

Residual | 30 | 4.04853937 | 0.134951 | |||

Total | 31 | 29.3996875 | ||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |

Intercept | 0.48715367 | 0.131420445 | 3.706833 | 0.000849 | 0.218757316 | 0.755550024 |

invoices | 0.012288152 | 0.000896554 | 13.70599 | 1.88E-14 | 0.010457145 | 0.014119159 |

SolutionB:

From the above output:

Regression eq is

**Time=0.4872+0.0123*invoices**

**slope=0.0123**

**y intercept=0.4872**

(c) At the level ? = 0.01, is there evidence of a linear effect of the number of invoices on the completion time? Answer based on the F test in ANOVA analysis

H0:There is no linear relationship between invoices and time

H1:There is linear relationship between invoices and time.

ANOVA | |||||

df | SS | MS | F | Significance F | |

Regression | 1 | 25.35114813 | 25.35115 | 187.854 | 1.87986E-14 |

Residual | 30 | 4.04853937 | 0.134951 | ||

Total | 31 | 29.3996875 |

F(1,30)=187.854

p=0.0000

p<0.01

Reject H0.

Accept H1

Conclusion:

there is sufficient evidence at 1% level of significance to conclude linear effect of the number of invoices on the completion time.

(d) Determine the coefficient of determination, ?2, and interpret its meaning (e

r sq=0.8623

86.23% variation in invoices is explained by model.

Good model

explained variance=86.23%

Unexplained variance=100-86.23=13.77%

e) Determine the standard error of estimate, and interpret its meaning

Se=0.3673572

(f) At the level ? = 0.01, conduct a t test about the population slope ?1

H0: no linear relationship exists between invoices and time

H0:?1=0

H1: linear relationship exists between invoices and time

H1:?1 not = 0

t=13.70599

p=1.8*106-14=0.0000

p<0.01

Reject H0.

Accept H1.

there is sufficient evidence at 1% level of significance to conclude that

linear relationship exists between invoices and time

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