In ramnathv/RGoogleForms: Generate Google Forms from an R Markdown File.

&text

Name

*** help

Please enter your name

# make this an external chunk that can be included in any file
options(width = 70)
opts_chunk$set(message = F, error = F, warning = F, echo = F, comment = NA, fig.align = 'center', dpi = 100, fig.height = 4.5, fig.width = 8)
source('~/Desktop/R_Projects/Code_Snippets/prob.R')
require(ggplot2); require(xtable); require(plyr); require(openintro)
options(xtable.type = 'html')
knit_hooks$set(inline = function(x) {
  if(is.numeric(x)) {
    round(x, getOption('digits'))
  } else {
    paste(as.character(x), collapse = ', ')
  }
})

--- &text

Email

*** help

Please enter your email

--- &radio

What can we say about the relationship between the correlation r and the slope b of the least-squares line for the same set of data?

*** items

1. Both r and b always have values between -1 and 1.
2. r is always larger than b.
3. r and b have the same sign (+ or -).
4. the slope b is always equal to the square of the correlation r.
5. b is always larger than r.

*** solution

The slope of the least squares line is given by $b = r \times s_y/s_x $. Clearly, $b$ can take values outside of $\pm 1$ and can be smaller, larger or equal to the correlation coefficient $r$. The only true statement is that both $b$ and $r$ must bear the same sign.

r 1 + 1

--- &checkbox

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of 290 and a standard deviation of 17. According to the standard deviation rule, almost 37.2% of the students spent more than

*** items

1. 256
2. 273
3. 307
4. 324
5. 341

*** solution

source('~/Desktop/R_Projects/Code_Snippets/prob.R')
gnorm(290, 17, quantile = 1 - 0.372)

--- &checkbox

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of 290 and a standard deviation of 17. According to the standard deviation rule, almost 37.2% of the students spent more than

*** items

1. 256
2. 273
3. 307
4. 324
5. 341

*** solution

source('~/Desktop/R_Projects/Code_Snippets/prob.R')
gnorm(290, 17, quantile = 1 - 0.372)

--- #college &radio

Can a college's acceptance rate be predicted by the Average SAT score of the students in that college? Here are the results from a sample of schools. Consider the problem of predicting Acceptance Rate (Y) from average SAT score (X). What would be the slope of the best fitting line to predict y from x?

      |SAT Score (X) | % Accepted (Y)

---------|------------- | ------------- Mean | 1264 | 38 Stdev. | 62 | 13 Correl. | -0.61

*** items

1. r -0.61^2
2. r -0.61*13/62
3. r -0.61*62/13
4. r -0.61*38/1264

*** solution

The slope of the least squares line is related to the correlation as $b = r \times \frac{s_y}{s_x}$. Plugging in the values from the table, we get $b = -0.61 \times \frac{13}{62}$, which equals r -0.61*13/62.

--- &radio #correlation1

Exercise 12

The correlation between two scores on tests was found to be exactly 1. Which of the following would not be true, regarding the corresponding scatterplot?

*** items

1. Every point would lie along a perfect straight line, with no deviations at all.
2. The slope of the best fitting line would be 1.
3. The best fitting line would have an uphill (positive slope).
4. All of the above are true.

*** solution

A correlation of 1 implies a perfect linear relationship meaning all points lie along a straigth line. Given that the correlation is positive, the line will slope uphill. However, there is no reason for the slope of the best fitting line to equal 1.

--- &radio

Let us enter the data on tests with:

t1 <- c(75, 85, 78, 82, 65, 85)
t2 <- c(90, 95, 87, 92, 94, 95)

Which command will do a two sample t test with an assumption of equal variances:

*** items

1. t.test(t1, t2)
2. t.test(t1, t2, var.equal=TRUE)
3. two.sample.t.test(t1,t2)

ramnathv/RGoogleForms documentation built on May 26, 2019, 10:14 p.m.