The Study of Houses' Price - Assignment Example

The paper "The Study of Houses' Price" is a wonderful example of an assignment on macro and microeconomics.

Price

Location

Custom

Square Metres

202500

1

0

126.945

193250

1

0

122.76

282250

0

0

158.1

309750

1

0

158.658

172500

1

1

125.364

174750

0

1

130.2

213750

1

0

176.7

217500

1

0

119.04

234750

0

0

132.804

205000

0

0

127.875

236250

0

0

146.94

243750

1

0

132.99

323750

0

1

348.75

423750

1

0

272.583

512500

1

1

246.45

135000

0

0

106.206

362250

1

1

159.03

181250

0

0

119.04

537500

1

1

271.653

218500

0

0

114.948

324750

1

1

255.099

167500

1

0

125.55

175000

0

0

139.965

262500

0

0

150.66

281250

1

1

159.03

233500

1

0

143.499

312500

1

0

199.95

154750

1

0

77.841

240000

1

0

146.289

317500

1

0

174.84

248750

1

0

139.5

218000

0

0

114.297

250000

0

0

142.755

199750

1

0

122.202

225000

1

0

130.2

284750

1

0

156.24

191500

0

0

111.6

145000

0

0

97.743

255000

0

0

149.358

219000

1

0

107.508

499750

1

1

239.94

182500

1

0

95.511

230500

1

0

123.318

243750

0

0

161.727

537500

1

1

247.752

312500

1

1

211.761

187500

1

0

124.434

399750

1

1

226.92

537500

1

1

264.864

300000

1

0

181.164

Task 1: Descriptive statistics

95% confidence interval for the prices of houses

The confidence interval means that we are 95% confident that the price of houses lies between.

Task 2: Hypothesis testing

Hypothesis testing is done as follows:

• Null and alternate hypotheses

• The and , the critical value is
• T-test is computed using as follows:

• Reject null hypothesis since falls in the critical region.
• There is sufficient evidence to show that the price of houses is $280,000.

Task 3

• Regression equation
• R-square value shows whether a model explains most of the variations in the data. A higher value of R-square indicates that a model explains most of the variation while a lower value indicates that a model explains less.
• The constant value of 21321 shows the price of a house with zero square meters. On the other hand, the slope indicates the rate at which price changes with a change in square meters.
• According to the regression output above, the standard error is 59192. It shows variability of points from the line of best fit. In this case, there is greater variability.
• In testing whether or not the coefficients of the slope are significant, the intention is to determine if the slope carries a different value from zero. During the process, a comparison is made between p-value and the level of significance. The p-value for the slope of the stock price index is approximately 0, which is less than the level of significance of 0.05. This indicates that the slope coefficient is significant at 0.05.
• Scatter plot of price vs square meters is displayed below

Coefficient of determination evidenced by summary regression output is 0.6931. This means that the fitted model explains only 69.31% of variability in exam scores.

• The regression equation is able to predict selling price for a house with 50 square meters. This is done as follows

• The other factor that can be included is distance from the urban centre.

Question 2

• Original Time Series Plot
• Time series plot of bookings versus time

• Summary of the plot

By observation, the plot above has a cyclical component with up and down movement around the trend. The fluctuations are equal across the period under investigation. Besides, it has a trend illustrated by an increasing long-term pattern.

• The first component that is visible is from the time series plot is trend. There is a gradual upward movement of the data over time. Secondly, the plot displays seasonality component. In this case, there is a pattern of fluctuation around the trend line with regular interval.
• 4 point centred moving average
• Smoothing the data using a 4 period centred moving average
• Time series plot that shows both the original and the 4-period centred moving average on the same plot

• The four-period
• Exponential smoothing

Alpha = 0.5

Alpha = 0.2

Original

Exponential smoothing with an alpha of 0.2 is the preferred option because it gives forecasts that closely reflect the actual values. This shows that values of low values of alpha have a greater smoothing effect.