This is the output of R. Please read the output and answer the questions below.

> summary(fit)

Call:

lm(formula = y~ ., data = dat)

Residuals:

Min1QMedian3QMax

-20.988-5.939-1.2264.212.39.053

Coefficients:

EstimateStd. Errort valuePr(>ItI)

(Intercept)15.43330.704821.897<2e-16 ***

x17.6702.0.98577.7824.08e-13***

x214.04040.979114.340<2e-16 ***

x3-0.71550.6303-1.1350.258

x4-0.24860.7164.-0.3470.729

---

Signif. codes:0'**'0.001 '**'0.01 '*'.0.05'.'0.1 ' '1

Residual standard error: 9.812 on 195 degrees of freedom

Multiple R-Squared: 0.7058,Adjusted R-squared:0.6998

F-statistic:117 on 4 and 195 DF, p-value: <2.2e-16

Is it right? The sample size is 200. The number of coefficients is 5. The most significant predictor is x2. The least significant predictor is x4.

Question1:

Suppose we now fit the following two simple regression models using the same data.

fit1 <- lm(y ~ x1)

fit3 <- lm(y~x3)

Statement:The R-squared value of fit1 is always larger than the R-Squared value of fit3.True or False?

Question 2:

Select all the correct statements.( Multiple correct)

A. We may increase the R-Squared of the model by removing some predictors.

B. If we use the best transformation found by the box-cox method, the R-Squared of the new model may be larger than the model showing above.

C. We may decrease the BIC value of the model by removing some predictors.

D. There may be multi-collinearity issues among the predictors.