Suppose we have:a response variable Y andan explanatory factor X with four levels.We ran the following code in R:mymodel <- lm(Y ~ X)Which of the following statements is FALSE.Group of answer choicesThe t value column of summary(mymodel) gives the t-statistic to test the null hypothesis that the true value of the regression coefficient is zero.By default, the estimated value of the intercept is the fitted value for the first level of X.The value of the fourth regression coefficient in the summary(mymodel) output is the estimated difference between the expected values of Y at level 4 and level 3 of X.mymodel has four regression coefficients.The Pr(>|t|) values in summary(mymodel) are the p-values for the null hypothesis that the true value of the regression coefficient is zero.

Suppose we have:a response variable Y andan explanatory factor X with  four levels.We ran the following code in R:mymodel <- lm(Y ~ X)What is the correct R code to test the null hypothesis that the expected value of Y does not depend on the level of X.Group of answer choicesplot(mymodel)anova(submodel,mymodel)t.test(mymodel)summary(mymodel)$coefanova(mymodel)

A UQ master student collected data on annual wages (Y, in $'000) and years of study (X) from a random sample of 10 part-time workers to test this proposition. Assuming a linear relationship between Y and X, the student used a least-squares method and found that the Y intercept = -21.50 and the slope = 9.73. The student also found that the standard error of the slope was 1.61. Based on this information, what is the value of the t test statistic if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? Round your final answer to three decimal places.

A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. The professor also found that the standard error of the slope was 0.08. Based on this information, what is the value of the t test statistic if you are testing the null hypothesis that there is no linear relationship between the two variables, X and Y? Round your final answer to two decimal places.

The overall regression F-statistic tests the null hypothesis that: a. all slope coefficients and the intercept are zero. b. all slope coefficients are zero. c. the slope coefficient of the variable of interest is zero, but that the other slope coefficients are not. d. the intercept in the regression and at least one, but not all, of the slope coefficients is zero.

Consider the following summary output for estimating the exam mark of a student based on their Stage I grade (A, B or C).> stage1.lm = lm(Exam ~ Stage1, data = course.df)> summary(stage1.lm)Call:lm(formula = Exam ~ Stage1, data = course.df)Residuals: Min 1Q Median 3Q Max -44.755 -9.352 1.818 9.420 29.478 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 68.755 2.003 34.331 < 2e-16 ***Stage1B -17.233 2.878 -5.988 1.64e-08 ***Stage1C -29.912 2.804 -10.666 < 2e-16 ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Residual standard error: 14.02 on 143 degrees of freedomMultiple R-squared: 0.4444, Adjusted R-squared: 0.4367 F-statistic: 57.2 on 2 and 143 DF, p-value: < 2.2e-16Give a point estimate of the mean exam mark for students who obtained an A in Stage 1. Give this to 1dp.