I have two assignment problems...
I have written this small code for regression with two regressors .
n <- 50
x1 <- runif(n,1,10)
x2 <- x1 + rnorm(n,0,0.5)
plot(x1,x2) # x1 and x2 strongly correlated
cor(x1,x2)
y <- 3 + 0.5*x1 + 1.1*x2 + rnorm(n,0,2)
intact.lm <- lm(y ~ x1 + x2)
summary(intact.lm)
anova(intact.lm)
the questions are
1.The function summary() is convenient since the result does not depend on
the order the variables
are listed in the linear model definition. It has a serious downside though
which is obvious in this case.
Are there any signficant variables left?
2. An anova(intact.lm) table shows how much the second variable contributes
to the result in
addition to the first. Is there a variable significant now?Is the second
variable significant?
the results i got:
> summary(intact.lm)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
Min 1Q Median 3Q Max
-5.5824 -1.5314 -0.1568 1.4425 5.3374
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.4857 0.9354 3.726 0.000521 ***
x1 0.2537 0.6117 0.415 0.680191
x2 1.3517 0.6025 2.244 0.029608 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.34 on 47 degrees of freedom
Multiple R-squared: 0.7483, Adjusted R-squared: 0.7376
F-statistic: 69.87 on 2 and 47 DF, p-value: 8.315e-15
> anova(intact.lm)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x1 1 737.86 737.86 134.7129 2.11e-15 ***
x2 1 27.57 27.57 5.0338 0.02961 *
Residuals 47 257.43 5.48
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
my question is that , i cant see any "serious downside" in using summary ().
And in the second question I am totally clueless. I need your help
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