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16.69
The independent variable (x) is “the floor number of the condominium” and the
dependent variable (y) is “the price (in $1,000)”. According to the given data, we find
the regression line:
3734
.
190
4654
.
1
ˆ
+
=
x
y
.
a.
H
0
: errors are normally distributed
H
1
: errors are not normally distributed
Since the number of standard residuals is larger than 30, we use chisquared test
for normality. With alpha = 0.05, we reject null hypothesis if statistic pvalue <
0.05.
All expected values are all larger than 5, so the “rule of five” is satisfied. It’s
valid to use chisquared test.
Since pvalue = 0.5079 > 0.05
, we fail to reject
the null hypothesis. Thus, we
conclude with 95 % confidence that there is insufficient evidence to infer errors
are nonnormal.
b.
Scatter diagram of standard residuals
3
2
1
0
1
2
3
150
170
190
210
230
250
Predicted dependent variable (Price)
Standardresiduals
The spread of points doesn’t change much when price varies. There is little sign
of heteroscedasticity.
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View Full Document16.77
The independent variable is “annual income (in $1,000)” and the dependent variable
is “weekly spent on food”. According to the given data, we find the corresponding
regression line:
8986
.
153
9582
.
1
ˆ
+
=
x
y
.
(i) First, we check whether errors are normally distributed:
H
0
: errors are normally distributed
H
1
: errors are not normally distributed
Since the number of standard residuals is larger than 30, we use chisquared test
for normality. With alpha = 0.05, we reject null hypothesis if statistic pvalue <
0.05.
All expected values are all larger than 5, so the “rule of five” is satisfied. It’s
valid to use chisquared test.
Since pvalue = 0.3618 > 0.05
, we fail to reject
the null hypothesis. Thus, we
conclude with 95% confidence that is insufficient evidence to infer errors are
nonnormal.
(ii) Next, we draw scatter diagram to diagnose heteroscedasticity:
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 Fall '11
 游啟璋

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