Analytical Approach to Economics and Finance - Assignment Example

ANALYTICAL METHODS IN ECONOMICS AND FINANCE Student Name Course Date ANALYTICAL METHODS IN ECONOMICS AND FINANCE PART A 1. The table below shows a summary of descriptive statistics for the dependent variable (housing prices): Descriptive Statistics for Housing Prices Mean 394.484 Standard Error 12.806 Median 385.000 Mode 320.000 Standard Deviation 89.640 Sample Variance 8035.387 Kurtosis -1.341 Skewness 0.128 Range 324.000 Minimum 241.000 Maximum 565.000 Sum 19329.700 Count 49.000 Mean: The mean is the average and is computed as the sum of all the observed outcomes from the sample divided by symbol for the by sample mean. The average of the total 50 observations of the housing prices, the average housing prices will be $ 394483 .Housing prices will be set with comparison of the calculated mean of the data of the quarterly reports. Standard Error: $ 12805 is the adjusting figures of the sample mean (394483) to achieve the real mean. It shows by how much the sample mean was close to the real mean. Median: The median is the middle score. Melbourne may choose a central or middle placed value of $ 385 for pricing of houses. Mode: It is value that occurs most in a distribution. Housing prices can be chosen from the most appearing price of the quarterly median prices .In this case $320 Standard Deviation: It is a measure that is used to quantify the amount of variation of asset of data. Variability of the prices from the mean is $ 89640 and it shows how much the prices vary from the mean prices. Kurtosis: It shows the sharpness of the peak of frequency distribution curve. The kurtosis of 1.34 shows that prices are relatively higher at the peak thus the distribution is not normal. Skewness: It is a measure of asymmetry probability distribution of a valued random variable around its mean .0.128 is the skewness which is above the normal distribution of zero the tail on the right side will be longer or fatter. 2. a) Probability that the House Price would be above $ 700,000 Probability for Therefore, probability that the house price would be above $ 700,000 is: b) Probability that a group of 20 houses will have an average house price of $ 500,000 Probability for Therefore, probability that the house price would be above $ 700,000 is: 3. An outlier is the data value that falls out of the shape of the distribution of a variable. It is an in indicator that a special case is worth investigation. It is a value that lies out of the normal distribution data. The outlier has minimal effect on the median. It is so because there is a lot of data clustered to the median making the effect slight on the median. The outlier is given weight as all other data in calculating the mean, hence it will be affected by the outlier either increasing the mean or making it low. The mean prices of housing would be therefore impacted by the outliers either prices would change either rise or fall. As compared to the mean, the prices of the median do not vary so much with the outliers. The median price will be better. PART B 1. 1) The independent variable is not strongly collinear. 2) The expected value of the residuals is always zero .The intercept is biased. 3) Homoskedasticity: The conditional variance of the error term is in constant X.Homo ske dasticity implies that the model uncertainty is identical in all observation. 4) Xi is deterministic: X is uncorrelated with the error term since xiis deterministic: Where X is determinant 5) Error term is independently distributed and not correlated. There is no correlation between the observations. 2. a priori expectations regarding the slope coefficients i) I expect to have a positive coefficient for interest. This is because, as interest rates rise, the mortgage rates also rise, leading to increased house prices. ii) HP = + GDP + е GDP Is expected to have a negative coefficient since improve GDP leads to improved disposable income and therefore more investment in real estate sector. This may increase the supply of houses and therefore reduce house prices. iii) HP = + FX + е There is expected to be a positive coefficient for foreign exchange. Increased exchange rates increase commodity prices, including the prices of houses. iv) HP = + POP + е Population change is expected to have a positive coefficient since increase in population pushes up the demand for houses and therefore increases their prices. 3. i) ii) iii) iv) 4. Interpretations i) The intercept (568.153) means that keeping interest as 0%, house prices will be $568,153. The coefficient -36.565 means that keeping all other factors constant, a change in interest by 1 will lead to a change in House prices by -$36565 ii) The intercept (449.189) means that keeping GDP as 0, house prices will be $449189. The coefficient -73.440 means that keeping all other factors constant, a change in GDP by 1 will lead to a change in House prices by -$73440 iii) HP = -37.118 + 522.876FX + е The intercept (-37.118) means that keeping GDP as 0, house prices will be $-37.118. The coefficient 522.876 means that keeping all other factors constant, a change in Foreign exchange by 1 will lead to change in House prices by $522876. iii) The intercept (178.967) means that keeping GDP as 0, house prices will be $178,967 The coefficient 140.579 means that keeping all other factors constant, a change in Foreign exchange by 1 will lead to change in House prices by $140579. 5. a) Whether Percentage Australian Population Change has statistically significant and positive effect on House Prices In this question, we find out whether percentage Australian population change has statistically significant and positive effect on house prices. i) 5% significance level For a 95% confidence interval, the t-critical value is ±1.96.   Coefficients Standard Error t Stat Intercept 178.9674892 53.16271451 3.3664099 POP (X) 140.5789807 33.91672804 4.1448273 (Population change has no effect on House Prices) H1 : ≠ 0 (Population change has effect on House Prices) . Hence, with 95% of confidence, we will reject the null hypothesis and say that population change has effect on House Prices. ii) 1% significance level For a 99% confidence interval, the t-critical value is ±2.576 (Population change has no effect on House Prices) (Population change has effect on House Prices) . Hence, with 99% of confidence, we will reject the null hypothesis and say that population change has effect on House Prices. b) Whether Interest Rate has statistically significant and negative effect on House Prices In this question, we find out whether interest rate has statistically significant and positive effect on house prices. i) 5% significance level For a 95% confidence interval, the t-critical value is ±1.96.   Coefficients Standard Error t Stat Intercept 568.1534395 44.66415036 12.72056974 INT (X) -36.56541747 9.105206733 -4.015879984 (Interest rate has no effect on House Prices) (Interest rate has effect on House Prices) . Hence, with 95% of confidence, we will reject the null hypothesis and say that interest rate has a negative effect on House Prices. ii) 1% significance level For a 99% confidence interval, the t-critical value is ±2.576 (Interest rate has no effect on House Prices) (Interest rate has effect on House Prices) . Hence, with 99% of confidence, we will reject the null hypothesis and say that interest rate has a negative effect on House Prices. PART C 1. a) b) MULTIPLE REGRESSION Regression Statistics Multiple R 0.978290731 R Square 0.957052755 Adjusted R Square 0.950917434 Standard Error 19.8594416 Observations 49 ANOVA   df SS MS F Significance F Regression 6 369133.8953 61522.31588 155.9906648 4.55413E-27 Residual 42 16564.69168 394.3974208 Total 48 385698.5869         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -571.5855604 160.1840727 -3.568304582 0.000914741 -894.8501065 -248.3210143 -894.8501065 -248.3210143 GDP 1.262408509 10.91146202 0.115695633 0.908445173 -20.75781334 23.28263036 -20.75781334 23.28263036 FX 82.86308701 57.56250487 1.439532334 0.157411911 -33.30275084 199.0289249 -33.30275084 199.0289249 CPI 13.77571284 6.936598535 1.985946392 0.053591858 -0.222909747 27.77433542 -0.222909747 27.77433542 INT -2.166506595 4.610937346 -0.46986251 0.640883797 -11.47175489 7.138741695 -11.47175489 7.138741695 POP -21.96613767 15.59500832 -1.408536451 0.166332455 -53.43813861 9.505863268 -53.43813861 9.505863268 Wages -3.156505889 5.097317939 -0.619248383 0.539097508 -13.44330995 7.130298176 -13.44330995 7.130298176 2. a) b) Explanatory power of the model The explanatory power of a regression model is measured by the coefficient of determination (R2). R2 gives the total variation in the dependent variable that can be explained by variation in the explanatory (independent) variables. Therefore, the explanatory power of this model is 0.957 as measured by the R2 shown above. This means that 95.7% of variation in House Prices can be explained by variations in the independent variables making up the model. c) 3. Why adding more variables into a model is a bad thing Adding more and more independent variables into a multi-variate regression model might be bad only if there is significant correlation between the new variable you want to add and the already existing variables in the model. This correlation will lead to changed values of the coefficients of the existing independent variables in the model. Read More