Estimate a multiple linear regression relationship with the U.K. stock returns as the dependent variable, and U.K. Governme
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Estimate a multiple linear regression relationship with the U.K. stock returns as the dependent variable, and U.K. Government Bond yield ( Interest rate), U.S. Stock Returns and Japan Stock Returns as the independent variables using the monthly data covering the sample period 1980-2019 (Finding the determinants of U.K. stock returns).
| Regression Statistics | ||||||||
| Multiple R | 0.728112444 | |||||||
| R Square | 0.530147732 | |||||||
| Adjusted R Square | 0.527180244 | |||||||
| Standard Error | 3.529169992 | |||||||
| Observations | 479 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 3 | 6675.354662 | 2225.11822 | 178.652021 | 1.566E-77 | |||
| Residual | 475 | 5916.144395 | 12.4550408 | |||||
| Total | 478 | 12591.49906 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -0.200685196 | 0.342405151 | -0.5861045 | 0.55808369 | -0.8735013 | 0.47213092 | -0.8735013 | 0.47213092 |
| RSUS | 0.704291096 | 0.041024277 | 17.1676661 | 9.5476E-52 | 0.62367959 | 0.7849026 | 0.62367959 | 0.7849026 |
| RSJA | 0.223877155 | 0.029524181 | 7.58284047 | 1.7922E-13 | 0.165863 | 0.28189131 | 0.165863 | 0.28189131 |
| RBUK | 0.041380786 | 0.04729839 | 0.87488783 | 0.38207709 | -0.0515592 | 0.13432074 | -0.0515592 | 0.13432074 |
a. Show the estimated regression relationship
b. Conduct a t-test for statistical significance of the individual slope coefficients at the 1% level of significance. Provide the interpretation of the significant slope estimates.
c. Conduct a test for the overall significance of the regression equation at the 1% level of significance. (Test for the significance of the regression relationship as a whole)
d. Present the R-Square Coefficient of Determinationand its interpretation.
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