\begin{shinyQuizBank}{postQuiz}
  \begin{shinyMCQ}{Simple regression is designed for:}
     \shinyMCAR{a quantitative IV and a quantitative DV.}{Yes!}
     \shinyMCAR{a categorical IV and a quantitative DV.}{Try again!}
     \shinyMCAR{a quantitative IV and a categorical DV.}{Try again!}
  \end{shinyMCQ}

  \begin{shinyMCQ}{The parameters in a simple regression model are:}
     \shinyMCAR{population values of intercept, slope, and error variance.}{Correct!}
     \shinyMCAR{sample estimates of intercept and slope}{No sample estimates are only
       uncertain approximations of the true, fixed population parameters.}
     \shinyMCAR{population values of intercept and slope.}{No, the error variance, $\sigma^2$,
        is also a parameter of the model.}
  \end{shinyMCQ}
  
  \begin{shinyMCQ}{The assumptions of simple linear regression are:}{fixed}
    \shinyMCAR{a. Normality of errors}{That is true, but incomplete}
    \shinyMCAR{b. Equal variance of errors}{That is true, but incomplete}
    \shinyMCAR{c. Linearity}{That is true, but incomplete}
    \shinyMCAR{d. Independent errors}{That is true, but incomplete}
    \shinyMCAR{e. Normality of the IV (x)}{That is not a regression assumption.}
    \shinyMCAR{d. a, b and c}{That is true, but incomplete}
    \shinyMCAR{f. a, b, c and d}{Correct!}
    \shinyMCAR{h. a, b, c, d and e}{Normality of the IV is not a regression assumption.}
  \end{shinyMCQ}
  
  \begin{shinyMCQ}{In simple linear regression:}
    \shinyMCAR{only linear relations can be modeled.}{That is not true.}
    \shinyMCAR{non-linear relations can be modeled by finding transformations of the IV and/or DV that have a linear relationship.}{Correct!}
  \end{shinyMCQ}

  \begin{shinyMCQ}{The independent errors assumption:}
    \shinyMCAR{can be checked with the residual vs. fit plot.}{No, that plot is used
      to check the linearity and equal variance assumptions.}
    \shinyMCAR{can be checked with the quantile-normal plot.}{No, that plot is used
      to check the normality assumption.}
    \shinyMCAR{cannot generally be checked with plots, but violations can sometimes
      be suspected from the story of how the experiment was conducted}{Correct!  
      If the same subject was used multiple times, or the subjects are grouped in 
      a nested (hierarchical) fashion, or the data represent the same outcome
      measured repeatedly over time, then the independent errors assumptions is
      probably violated.}
  \end{shinyMCQ}
  
  
  \begin{shinyMCQ}{Which of the following is a possible model equation?}
    \shinyMCAR{$y = b_0 + b_1 x + \epsilon$}{No, model equations use parameters, not estimates}
    \shinyMCAR{$y = \hat{\beta_0} + \hat{\beta_1} x + \epsilon$}{No, model equations use parameters, not estimates}
    \shinyMCAR{$y = \beta_0 + \beta_1 x + \epsilon$}{Correct!}
  \end{shinyMCQ}
  
  \begin{shinyMCQ}{Which of the following is a possible prediction equation?}
    \shinyMCAR{$y = \beta_0 + \beta_1 x + \epsilon$}{No, prediction equations cannot include $\epsilon$.}
    \shinyMCAR{$y = b_0 + b_1 x$}{Correct!}
    \shinyMCAR{$y = b_0 + b_1 x + \epsilon$}{No, prediction equations use estimates, not parameters.}
  \end{shinyMCQ}

  \begin{shinyMCQ}{If the model assumptions are NOT met reasonably well then:}{fixed}
    \shinyMCAR{the standard errors are incorrect.}{That is true, but incomplete.}
    \shinyMCAR{the p-values are incorrect.}{That is true, but incomplete.}
    \shinyMCAR{the confidence intervals are incorrect.}{That is true, but incomplete.}
    \shinyMCAR{all of the above.}{Good work!}
  \end{shinyMCQ}

  \begin{shinyMCQ}{If the null hypothesis for the slope ($H_0: \beta_1=0$) is true and if model assumptions are met reasonably well then:}{fixed}
    \shinyMCAR{a. if you could repeat the experiment many times about 5\% of the p-values would
        be $<=0.05$.}{That is correct, but incomplete.}
    \shinyMCAR{b. if you could repeat the experiment many times about 95\% of the 95\% confidence
        intervals would contain the true value of $\beta_1$}{That is correct, but incomplete.}
    \shinyMCAR{c. the power of the test is 95\%.}{No.  Power is immaterial when the null hypothesis
      is true (or by some definitions the power is 5\%).}
    \shinyMCAR{c. a and b}{Correct!}
    \shinyMCAR{e. a, b and c}{No, you are claiming too much!}
  \end{shinyMCQ}
  
  \begin{shinyMCQ}{If the alternative hypothesis for the slope ($H_A: \beta_1 \ne 0$) is true 
    and if model assumptions are met reasonably well then:}
    \shinyMCAR{the chance of correctly rejecting the null hypothesis is 95\%}{No, that chance
       depends on the power of the experiment, which in turn depends on samples size, error
       variance, true effect size, and spread of the IV values.}
    \shinyMCAR{Additional information is needed to determine the chance of correctly rejecting
       the null hypothesis.}{Correct, that chance
       depends on the power of the experiment, which in turn depends on samples size, error
       variance, true effect size, and spread of the IV values.}
  \end{shinyMCQ}

  \begin{shinyMCQ}{The slope estimate, $b_1$:}
    \shinyMCAR{is a biased estimate of $\beta_1$}{No, it is unbiased if the model linearity assumption is correct.}
    \shinyMCAR{is a point estimate of the mean of the DV when the IV equals 0.}{No, that is the
    interpretation of the intercept.}
    \shinyMCAR{is a point estimate of the change in the mean of the DV when the IV increases by 1.}{Correct!}
  \end{shinyMCQ}

  \begin{shinyMCQ}{The intercept p-value is meaningful only if:}{fixed}
    \shinyMCAR{a. there is data near x=0.}{That is true, but incomplete.}
    \shinyMCAR{b. before the experiment is run, both $H_0: \beta_1=0$ and
                  $H_A: \beta_1 \ne 0$ are scientifically meaningful and are possible.}{That is true, but incomplete.}
    \shinyMCAR{c. both a and b}{Excellent!}
  \end{shinyMCQ}

\end{shinyQuizBank}
