Linear Regression with Excel [cf Chps 19 - 27]
Explanatory comments appear in bold font
Y data X data
Inflation Unemployment Labels
4.2 6.0
3.5 5.5
2.8 6.1 Question: What is the degree of association between
3.2 7.0 unemployment and inflation?
3.1 4.8
4.2 6.0 Is unemployment a good predictor of inflation?
5.0 7.2
3.8 4.3
4.5 5.0
3.9 3.8
4.1 6.0
6.0 7.1
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 0.052254262
Standard Error 0.8569058 rms error for Inflation [Y-] estimates
Observations 12
ANOVA
df SS MS FSignificance 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 5.37278733
Unemployment 0.298639113 0.235617681 1.267473269 0.233704823 -0.226349888 0.823628114 -0.226349888 0.823628114
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.]
