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A step-by-step guide on how to perform a multiple linear regression analysis using excel to examine the relationship between inflation, unemployment, and per capita gnp. The analysis includes the calculation of regression statistics, anova, and coefficients with their standard errors, t-statistics, p-values, and 95% confidence intervals. The study aims to determine the degree of association between the variables and their predictive power of inflation.
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Linear Regression with Excel [cf Chps 19 - 27] Explanatory comments appear in bold font Y data X data Inflation Unemployment Labels 4.2 6. 3.5 5. 2.8 6.1 Question: What is the degree of association between 3.2 7.0 unemployment and inflation? 3.1 4. 4.2 6.0 Is unemployment a good predictor of inflation? 5.0 7. 3.8 4. 4.5 5. 3.9 3. 4.1 6. 6.0 7. SUMMARY OUTPUT Tools: Data Analysis: Regression Labels: On ; Line fit plot: Off ; Residuals: Off; Residual plot: Off ; New workbook Regression Statistics Multiple R 0.37203893 Absolute value of the correlation coefficient R Square 0.138412965 [Note: The sign of r can be determined from the information below.] Adjusted R Square 0. Standard Error 0.8569058 rms error for Inflation [Y-] estimates Observations 12 ANOVA df SS MS F Significance F F test is another type of test of Regression 1 1.179624496 1.179624496 1.606488487 0.233704823 significance that takes as a NH that Residual 10 7.342875504 0.73428755 r = 0. That is, unemployment is not Total 11 8.5225 a good predictor of inflation. Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.312802419 1.373336486 1.684075566 0.123072411 -0.747182491 5.37278733 -0.747182491 5. Unemployment 0.298639113 0.235617681 1.267473269 0.233704823 -0.226349888 0.823628114 -0.226349888 0. Regression line equation: Inflation = (2.31) + (.299)*Unemployment Standard error for the coefficients t-statistic for the NH that the coefficient is 0 P-value for the NH that the coefficient is 0 95% CI for the coefficients [The sign on the coefficient of the independent variable [Unemployment] is the same as the sign of r.]
Multiple regression with Excel Explanatory comments appear in bold font Y data X1 data X2 data Inflation Unemployment Per capita GNP Labels 4.2 6.0 11. 3.5 5.5 10. 2.8 6.1 10.9 Question: What is the degree of association 3.2 7.0 9.8 between unemployment, per capita GNP and inflation? 3.1 4.8 12. 4.2 6.0 13.1 Are unemployment and GNP good predictors of inflation? 5.0 7.2 13. 3.8 4.3 10. 4.5 5.0 12. 3.9 3.8 8. 4.1 6.0 9. 6.0 7.1 12. SUMMARY OUTPUT Tools: Data Analysis: Regression Labels: On ; Line fit plot: Off ; Residuals: Off; Residual plot: Off ; New workbook Regression Statistics Multiple R 0.495269464 Correlation coefficient R Square 0.245291842 [r has no sign in the context of a multiple regression analysis] Adjusted R Square 0. Standard Error 0.845379617 rms error for Inflation [Y-] estimates Observations 12 ANOVA df SS MS F Significance F F test is another type of test of Regression 2 2.090499725 1.045249862 1.462569708 0.281841992 significance that takes as a NH that Residual 9 6.432000275 0.714666697 r = 0. I.e. unemployment and GNP Total 11 8.5225 are not good predictors of inflation. Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.722477154 1.954481569 0.369651556 0.720190238 -3.698870696 5.143825004 -3.698870696 5. Unemployment 0.168577571 0.259431005 0.649797317 0.532055919 -0.418296582 0.755451723 -0.418296582 0. Per capita GNP 0.209195054 0.185299283 1.128957709 0.288108138 -0.209981366 0.628371475 -0.209981366 0. Regression line equation: Inflation = (.722) + (.169)Unemployment + (.209) GNP Standard error for the coefficients t-statistic for the NH that the coefficient is 0 P-value for the NH that the coefficient is 0 95% CI for the coefficients