# Multiple Regression

Topics: Regression analysis, Errors and residuals in statistics, Linear regression Pages: 5 (1075 words) Published: December 18, 2012
Multiple Regression Analysis of exchange rate with the determinant factors

Regression Analysis: USD versus GDP Growth, FER, FDI Growth, Interest Rate, Money Supply, Terms Of Trade

The regression equation is
USD = 41.5 - 1.95 GDP Growth + 0.000943 FER - 0.139 FDI Growth + 0.048 Differential Interest Rate + 0.000067 Money Supply + 0.166 Terms of Trade - 0.000097 External Debt |

Predictor T PConstant 2.32 0.039GDPGrowth -3.43 0.005 FER 1.01 0.332FDIGrowth -1.55 0.146Differential Int Rate 0.11 0.913Money Supply 0.89 0.393Terms of Trade 0.35 0.731External Debt -0.73 0.479|

Where,
|
T is t stat. T-stat is a measure of the relative strength of prediction (is more reliable than the regression coefficient because it takes into account error).| The p-value is a percentage. It tells you how likely it is that the coefficient for that independent variable emerged by chance and does not describe a real relationship. A p-value of .05 means that there is a 5% chance that the relationship emerged randomly and a 95% chance that the relationship is real.|

Calculating, Co-efficient of determination

S = 2.07927 R-Sq = 85.0% R-Sq(adj) = 76.2%

Analysis of Variance

Source DF SS MS F P
Regression 7 293.031 41.862 9.68 0.000
Residual Error 12 51.881 4.323
Total 19 344.912

Interpretation of the Regression Model for USD

a) The P value is equal to 0.006. It indicates that model fit for regression equation is acceptable. b) The R Squared (adjusted) value is 76.2% showing that the determination coefficient is high and regression line fits the data well. Also it shows that well future outcomes are likely to be predicted by the model ie, value of USD can be predicted using this equation c) As per the P values of GDP Growth (0.005), it is evident that GDP Growth has significant impact on USD exchange rate in INR where as others have insignificant impact.

d) Now the regression equation shows that GDP is 1.95 times inversely proportional to USD which means that with fall on GDP, rupee will get weaker and result in rise in exchange rate for USD. e) The other two factors that are showing significant values in the equation are terms of trade and FDI growth but the relationship as depicted by the P value is low.

Regression Analysis: GBP versus GDPGrowth, FER, FDI Growth, Interest Rate, Money Supply, Terms Of Trade

The regression equation is

GBP = 28.4 - 2.14 GDPGrowth + 0.00215 FER + 0.304 FDIGrowth - 0.59 Differential Int Rate + 0.000132 Money Supply + 0.98 Terms of Trade - 0.000135 External Debt | |

Predictor Coef SE Coef T P Constant 28.41 47.18 0.60 0.558 GDPGrowth -2.138 1.425 -1.50 0.159 FER 0.002152 0.002153 1.00 0.337 FDIGrowth 0.3036 0.2209 1.37 0.194 Differential Int Rate -0.592 1.731 -0.34 0.738 Money Supply 0.0001319 0.0002098 0.63 0.541

Terms of Trade 0.978 1.106 0.88 0.394
External Debt -0.0001349 0.0003145 -0.43 0.676

Calculating, Co-efficient of determination

S = 4.90981 R-Sq = 61.8% R-Sq(adj) = 39.6%

Analysis of Variance

Source DF SS MS F P
Regression 7 468.48 66.93 2.78 0.058
Residual Error 12 289.27 24.11
Total 19 757.76

Interpretation of the Regression...