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Q1 and Q2

House Price
67000 Question 1: Calculate the 95% confidence limits for the population mean of house prices.
68000 It is given that the population standard deviation is equal to $45000.
68000
69000
72000 8820 lower limit 115061.5
75000
76000 Upper Limit 132701.5
76900
77000
78000 If Sigma was not given, use data anlaysis to get this (below)
79000
80000
80000 House Price
81000
82000 Mean 123881.5
83000 Standard Error 4457.1477412549
84000 Median 106500
84000 Mode 102000
86250 Standard Deviation 44571.4774125491
87000 Sample Variance 1986616598.73737
89500 Kurtosis 1.0548503827
90400 Skewness 1.1646598578
90500 Range 188000 Upper 115037.551896077
91000 Minimum 67000
91500 Maximum 255000 Lower 132725.448103923
91500 Sum 12388150
92500 Count 100
93500 Confidence Level(95.0%) 8843.9481039231
93500
94000
95500
96000
96000
97900 Question 2: It is claimed that the average house price is $125K or less. Set up the null and alternate hypotheses and
98000 conduct the test at the alpha of 0.05. It is given that the population standard deviation is equal to $45000.
98000
98000
99000 Ho = Mu LE 125K
99000
99000 H1= Mu GT 125K
102000
102000
102000 Xbar 123881
102000 n 100
103000
103000
103500 Zstat -0.2486666667
103500
105000 Z critical 1.646 for the alpha of 0.05
105000
108000 Accept the null hypothesis.
112000
112500 Conclusion: The claim that the mean house price is 125K 0r below is correct.
114900
115500
120500
122000
125500
127000
128000
129900
130350
132350
133000
134500
135500
135500
136500
136500
137400
137400
137500
139500
144000
145000
149000
155000
154000
155500
156500
163000
165000
167000
168700
169900
169900
169900
176000
179000
179000
179500
179500
187500
203000
220000
222000
250000
250000
255000
255000

Q3 Solution

t-Test: Two-Sample Assuming Unequal Variances
Location 2 Location 3 Ho Mu2 =Mu3
Mean 88377.7777777778 101312.5 H1 Mu2 NE Mu3
Variance 267547179.487179 201860967.741935
Observations 27 32 Two tail test
Hypothesized Mean Difference 0
df 52 Tstat -3.2119420179
t Stat -3.2119420179
P(T<=t) one-tail 0.0011318082 Tcritical 2.0066468051 -2.0066468051
t Critical one-tail 1.6746891537
P(T<=t) two-tail 0.0022636164 Tstat is outside the acceptance range, hence we reject the null hypothesis.
t Critical two-tail 2.0066468051
Conclusion: The two means are different.

Q4 Solution

Q4
SUMMARY HO Mu1 =Mu2=Mu3=Mu4=Mu5
Groups Count Sum Average Variance
Location 1 8 747500 93437.5 26941964.2857143 H1 Not all means are equal.
Location 2 27 2386200 88377.7777777778 267547179.487179
Location 3 32 3242000 101312.5 201860967.741935
Location 4 24 3746600 156108.333333333 458024275.362321
Location 5 9 1963500 218166.666666667 1462250000
ANOVA Since Fstat is above Fcritical, we reject the Ho,
Source of Variation SS df MS F P-value F crit
Between Groups 161766824850 4 40441706212.5 107.8140782368 1.93306561967325E-34 2.4674936234 Hence not all the means are equal.
Within Groups 35635068750 95 375105986.842105
Total 197401893600 99

Q3 and Q4

Location 1 Location 2 Location 3 Location 4 Location 5
86250 67000 75000 120500 165000 Question 3: Using the t test, test the claim that the average housing prices of location 2 and location 3
86250 68000 78000 128000 167000 are not different. Write the hypotheses, etc.
90000 68000 81000 134500 179500
95000 69000 87000 135500 220000
96000 72000 89500 136500 222000
97000 76000 90500 136500 250000
98000 76900 91000 137400 250000
99000 77000 91500 137500 255000
79000 91500 144000 255000
80000 92500 145000
80000 95500 149000
82000 97900 155000
83000 98000 154000
84000 98000 156500
84000 99000 163000
90400 99000 169900
93500 102000 169900
93500 102000 169900
96000 102000 176000
96000 103000 179000
98000 103000 179000
99000 103500 179500
102000 103500 187500
108000 105000 203000
114900 105000
122000 112000
127000 112500
115500
125500
129900
130350 Question 4: Using the ANOVA, test the claim that the average housing prices of all these locations are different.
132350 Wrtie the hypothese,etc..

Q5 solution

SUMMARY OUTPUT
Ho Slope B1 =0
Regression Statistics H1 Slope B1 NE 0
Multiple R 0.3961102897
R Square 0.1569033616
Adjusted R Square 0.1483003347 equation
Standard Error 41133.9360170468
Observations 100 Yhat = 27754.9 +29396.5 X
ANOVA It is significant since we reject the Ho (Fstat > Fcritical)
df SS MS F Significance F
Regression 1 30858975434.0591 30858975434.0591 18.2381576883 0.0000451375 Fcritical ~4
Residual 98 165816067840.941 1692000692.2545 for alpha of 0.05; df1 =1 and df2 = 98.
Total 99 196675043275
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Rsquare = 0.1569.
Intercept 27754.9005880707 22881.6048896187 1.212978754 0.2280536798 -17652.8996222996 73162.700798441 -17652.8996222996 73162.700798441 15.69% of the total variation is explained by the
Bedrooms 29396.5135816297 6883.4370185067 4.27061561 0.0000451375 15736.5568432443 43056.4703200152 15736.5568432443 43056.4703200152 regression equation.
Yhat for X=4 145340.95491459

Q5

House Price Location Bedrooms Bathrooms
67000 2 2 1 Question 5: It is believed the price of a house is related
68000 2 3 1 the number of bedrooms.
68000 2 3 1 (a) Perform a regression analysis to determine such a relationship.
69000 2 2 1 (b) Write down the equation. Is the relationship significant? Why?
72000 2 4 2 © What is the interpretation of R-Square?
75000 3 2 1
76000 2 2 1 (d) What will the predicted price of the house that has 4 bedrooms?
76900 2 3 1
77000 2 2 3
78000 3 2 1
79000 2 3 2
80000 2 3 1.5
80000 2 3 1
81000 3 2 1
82000 2 3 1.5
83000 2 3 1
84000 2 3 1
84000 2 3 1.5
86250 1 4 2
87000 3 3 2
89500 3 3 2
90400 2 4 2
90500 3 3 1.5
91000 3 3 2
91500 3 4 2
91500 3 4 2
92500 3 3 1.5
93500 2 3 2
93500 2 4 2
94000 1 3 1.5
95500 3 3 2
96000 2 3 2
96000 2 3 2
97900 3 3 2
98000 3 3 2
98000 2 3 2
98000 3 3 2
99000 2 4 2
99000 3 4 2
99000 3 3 2
102000 3 4 2
102000 2 3 1.5
102000 3 4 2
102000 3 3 1.5
103000 3 3 2
103000 3 3 1.5
103500 3 3 2
103500 3 3 2
105000 3 3 2
105000 3 3 1.5
108000 2 3 2
112000 3 4 2
112500 3 3 2
114900 2 5 2
115500 3 4 2
120500 4 3 2
122000 2 3 3
125500 3 4 2.5
127000 2 3 2.5
128000 4 3 2
129900 3 4 2.5
130350 3 3 2
132350 3 3 2
133000 3 3 2
134500 4 3 2
135500 3 3 3
135500 4 3 3
136500 4 3 2
136500 4 3 2
137400 3 4 2.5
137400 4 4 2.5
137500 4 3 2
139500 3 4 2.5
144000 4 4 2.5
145000 4 3 2
149000 4 3 2
155000 4 4 2
154000 4 3 2
155500 3 3 2.5
156500 4 3 2
163000 4 4 2
165000 5 4 2
167000 5 4 2
168700 3 3 2.5
169900 4 4 2.5
169900 4 3 2.5
169900 4 3 2.5
176000 4 4 2.5
179000 4 4 2.5
179000 4 4 2.5
179500 4 3 2.5
179500 5 3 2.5
187500 4 4 2.5
203000 4 4 3
220000 5 4 3.5
222000 5 3 3.5
250000 5 4 2.5
250000 5 4 2.5
255000 5 4 2.5
255000 5 3 2.5