Question - Most of the time houses prices depend on the local market conditions. In addition one of the factors is the number of bedrooms (as bedrooms increase prices increases). Recently Come Real Estate Agency has conducted a survey and selected a random sample of 211 for July 2015 sale in Melbourne and the data analyzed is summarized as follows.
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SUMMARY OUTPUT
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Regression Statistics
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Multiple R
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0.817326539
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R Square
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0.668022671
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Adjusted R Square
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0.66615763
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Standard Error
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115.8071494
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Observations
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180
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ANOVA
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df
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SS
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MS
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F
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Significance F
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Regression
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1
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4803674
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4803674
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358.1811918
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1.74254E-44
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Residual
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178
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2387211
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13411.3
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Total
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179
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7190885
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Coefficients
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Standard Error
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t Stat
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P-value
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Lower 95%
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Upper 95%
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Lower 95.0%
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Upper
95.0%
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Intercept
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-137.8814237
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25.56878832
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-5.39257
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2.18686E-07
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-188.3383819
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-87.4244654
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-188.3383819
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-87.424465
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Bedrooms
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178.6267021
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9.438326385
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18.92568
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1.74254E-44
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160.0012892
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197.252115
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160.0012892
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197.25212
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House Price
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Mean
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317.6166667
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Standard Error
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14.93923611
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Median
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271.8
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Mode
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230.5
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Standard Deviation
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200.4308849
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Sample Variance
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40172.53961
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Kurtosis
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9.869866365
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Skewness
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2.287541039
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Range
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1544.3
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a) Write down the regression equation.
b) State the R-squared value and the standard error and explain what they mean with respect to the data.
c) Write down the value of the gradient of the regression line and explain what it means for this data.
d) Are the values for the constant and the gradient (slope) significant (i.e. significantly different from zero) in this case? Justify your answer.
e) Conduct a hypothesis test on the slope coefficient to test whether there is a linear relationship between number of bedrooms and prices of the houses. Include the null and alternative hypotheses; key test results and an appropriate conclusion.
f) Does the linear regression provide a good model? Give statistical reasons based on the scatterplot, p-values, the standard error and coefficient of determination.
g) If you were developing a model to predict the prices of the houses on the number of bedrooms, what other factors would you like to be able to include?