In linear regression, the predicting variables and the response variable are all random variables.

In ANOVA, the greater the value of the F ratio (MSTr/MSE), 

Part 2 – Multiple Choice

We will find significant differences across the means if the between-group variability is smaller than the within-group variability in ANOVA.

A high Adjusted R-squared value does not mean that a linear regression model is a good fit to the data set used to estimate the model.

One of the primary objectives of ANOVA is to test the null hypothesis that all the sample means are different vs the alternative that at least two of the means are equal.

Questions 22-25 A linear regression model was fitted to estimate the response variable Cirrhosis.Death.Rate using the percentage of the population who was urban, and wine and liquor consumption per capita.  There are 46 data points in this model. Using the following R output from a fitted multiple linear regression model, answer the following multiple-choice questions. Call:lm(formula = Cirrhosis.Death.Rate ~ ., data = data)Residuals:     Min       1Q   Median       3Q      Max -28.5939  -5.0002   0.7397   7.2051  18.1331 Coefficients:                              Estimate Std. Error t value Pr(>|t|)    (Intercept)                     3.8706     7.1618   0.540 0.591738    Percent_Population_Urban        0.4965     0.1414   3.512 0.001078 ** Wine_Consumption_per_capita     1.6008     0.3919   A   0.000194 ***Liquor_Consumption_per_capita   0.2286     0.1002   2.281 0.027702 *  —Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 10.96 on C degrees of freedomMultiple R-squared:  0.796,    Adjusted R-squared:  B F-statistic: 54.62 on 3 and C DF,  p-value: 1.503e-14

Controlling variables are variables which are used to help researchers control bias selection in the response data, thus should be discarded from the model when conducting multiple linear regression.

In linear regression, the assumption of normality is required for reliable derivations of confidence intervals, prediction intervals, and hypothesis testing. 

When checking for outliers using Cook’s distance, one rule of thumb commonly used for small sample data is to investigate any outliers with a Cook’s Distance greater than .