Explain in one sentence. Include the corresponding teststatistic, degrees of freedom and Pvalue
in your answer.
e) Examine the distribution of the residuals and plot the residuals versus each of the explanatory
variables. Describe your findings. Does your analysis suggest that the model assumptions may
not be reasonable for this problem? Explain.
f) Fit a regression model to predict
Rent
using only
Vacancy
. Explain why the coefficient for
years in rank and the results of a significance test for this coefficient differ from what you found
in parts (a) and (d) above.
g) Give an approximate 95% prediction interval for the office rent in a city whose vacancy rate is
10% and whose unemployment rate is 7%.
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Question 4 – Simple Linear Regression MS Excel Template
Below is the template for the output from simple regression using MS Excel. But instead of
actual results, the cells are numbered from (1) to (27). Your task is to provide the formulas used
to compute each of the cell entries. You can answer this in neat handwritten form; you do not
need to type the formulas! Just write each cell number and the corresponding formula after it.
Some of these statistics can be obtained by more than one formula. Any correct formula is
acceptable. Some of these are most easily obtained from other cells in the table. If so, use "Cell
X" as part of your formula.
Note: This will be excellent practice for the final exam. We suggest that you keep a copy of your
answers to this question as a formula sheet for the exam.
SUMMARY
OUTPUT
Regression
Statistics
Multiple R
(1)
R Square
(2)
Adjusted R
Square
(3)
Standard Error
(4)
Observations
(5)
ANOVA
df
SS
MS
F
Significance
F
Regression
(6)
(7)
(8)
(9)
(10)
Residual
(11)
(12)
(13)
Total
(14)
(15)
Coefficient
s
Standard
Error
t Stat
P
value
Lower 95%
Upper
95%
Intercept
(16)
(17)
(18)
(19)
(20)
(21)
X Variable
(22)
(23)
(24)
(25)
(26)
(27)
*** END ***
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 Winter '10
 E.Fowler
 Statistics, Regression Analysis, Statistical hypothesis testing, size

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