Introduction

This is a report of the regression analysis questions done using Stata software. The questions were part of the 5 exam questions that were to be completed by students. Of the 5, questions 1, 3 and 5 five required the use of the software to run regression analyses for various subsets of the questions and use the results to answer them as well as other question subsets. This report is therefore specifically dedicated to the 3 questions stated above. Each of them is discussed under their specific subsections as indicated below:

Question 1: Determinants of median house prices in neighborhoods

This question required the use of regression analysis to establish determinants of house prices in 506 neighborhoods. The table below shows the outcome of the regression analysis (Wang & Li , 2016)

1. As seen from the table, all the factors are significant in influencing the median price of houses in these neighborhoods. This is confirmed by the p>|t| column which describes the significance of the coefficients of each variable the significance is usually compared against a preset level (mostly 0.05). if the p-value is less than the set level, then we conclude that the variables are significant in predicting the outcome of the dependent variable (Bianco , et al., 2013). Of all these variables, rooms and radial have positive influence on the median house prices. The remaining variables all negatively influence the median house prices. That is, an increase any of the factors leads to a decrease in house prices.
2. The regression equation is as given below;

Price =  27433.93 -189.4686 crime  -2722.128nox +  6392.374rooms  -1051.506dist + 292.5661  radial -132.3062proptax  -1229.857stratio

1. This yields the following results given the features of 130 street.

Price = 27433.93 -189.4686 *0.881  -2722.128* 6.24 +  6392.374*5.64  -1051.506*1.98 + 292.5661*4 -132.3062*43.7  -1229.857*21.2

• Price = 13,567.50. So according this result, the board members are not justified in their belief as at the current price of 14,300the house is marginally overpriced.
• The resulting value from this change according to the previous equation is 14,030 which is a marginal increase from the previous prediction but still lower than the current real-life property value. Therefore, based on the real property value, this claim is also not justified.
• Again, the result is 13,091.5 which is lower than both the predicted and the real property value. Therefore, this move would be counterproductive as it will reduce the property value.

Question 3: The Phillips curve

1. The results of the regression analysis are as shown in the below table

This yields the following relationship below

Inf_rt – 1.143389infexply = 1.24 – 0.3025(urate – u*)

This implies that an increase in unemployment by a single point causes a 0.3025 reduction in unanticipated inflation.

• The implied natural rate of inflation is estimated as follows:

U* = -1.143389 – (-0.3025)

      = -0.8409

• The results of the new regression are as per the below table;

The resulting equation is; inf_rt – 0.06465infexply = 2.8142 – 0.1555(urate – u*)

Which is clearly different from the equation obtained in the previous question. This implies that even though the relationship between inflation and unemployment remains negative, it tends to zero as time goes by and will likely be positive in the future given the relationship trend from the two equations specified above.

• The revised results are as shown in the below table;

From the above table, we estimate the Phillip’s curve equation as below;

Inf_rev – 1.0925infexply = 1.46 – 0.297 (urate – u*)

This equation is marginally different from that obtained in part a as are the results shown in the outcomes table. All the point estimates are marginally smaller compared to those obtained in part a above.

• The implied natural rate of unemployment is calculated as below

U* = -1.0925 – (-0.297)

     = -0.7955.

Compared to the results in part b, the implied natural rate of unemployment is marginally lower when the data is adjusted for measurement error issues.

Question 5: Risky capital in emerging markets

1. The regression results for verifying empirical fact (i) are as displayed in the table below;

Portfolio 2 is the base portfolio.

From the results in the table above, portfolio 1 which represents emerging markets has a coefficient of 0.01434 while portfolio 3 representing wealthier markets has a coefficient of -0.01783 which is almost twice as low as that of portfolio 1. This therefore verifies empirical fact (i) and confirms that indeed, emerging markets exhibit averagely higher returns to capital.

•  The results are as shown in the two table below;

From the first table, portfolio 1 has a negative coefficient while portfolio 3 from the second table has a positive coefficient when US returns are regressed against them. This implies that emerging markets are more responsive to US returns as they are negatively affected while wealthier markets tend to marginally increase with increase in Us returns. As such we conclude that emerging markets are more highly exposed to US returns than wealthier markets. This verifies empirical fact (ii) as was stated.

• The results of this regression are s shown in the table below;

As seen from the table, the coefficient of returns which represent emerging markets are positive in relation to the US returns while the portfolio coefficient is still negative as was obtained in part b. On the other hand, the coefficient of portfolio 3 representing wealthier markets still remains positive. The latter two observations are in line with those made in part b above which verifies empirical fact (ii) while the former observation are in line with observations made in part a which verifies empirical fact 1. Thus, all the two empirical facts are verified.

References

Bianco , V., Manca, O. & Nardini, S., 2013. Linear Regression Models to Forecast Electricity Consumption in Italy. Energy Sources Part B Economics Planning and Policy.

Wang , T. & Li , Z., 2016. Outlier detection in high-dimensional regression models.. Communication in Statistics- Theory and Methods.