(15-20 min)

Use this Shiny app to answer the next three questions. http://sites.uclouvain.be/selt/files/medias/unamur-regression-lineaire-module20.swf

Each person do these, have your partner check your work. Give each other a thumbs up when you’ve got it!

- With 3 points, use the arrow controls in the bottom-right to move and rotate the line to have y = 0 + 1 x with mean \(\bar{x}=100\) and \(\bar{y}=100\), and \(r=1\) (slope and correlation should be exact, intercept and means should be within 1 unit).

(If you accidentally move the points off the line, update the number of points twice to have the points replaced on the line.)

Click the leverage button. Leverage is a measure of how much a point is an outlier (extreme) in the \(x\) direction. It’s called leverage because points with high leverage potentially have a lot of influence on the regression line slope, pulling it up or down like a lever.

With 5 points, move the points to have correlation \(r=-0.5\), one point has huge leverage and the rest have small leverages.

With 5 points, move the points to have correlation \(r=-0.5\), each point has roughly equal leverage — largest diameter not more than 3x the smallest.

Move the points to make \(r < 0\) and a positive slope.

(2 p) Write regression equation.

(2 p) Interpret slope.

(2 p) Interpret R2

(3 p) Complete this table of predictions.

`agewks` |
`shearpsi` |
---|---|

5 | ? |

20 | ? |

40 | ? |

- (1 p) Predictions: How comfortable do you feel about each of these predictions?
`agewks`

= 5:`agewks`

= 20:`agewks`

= 40:

A rocket motor is manufactured by bonding an igniter propellant and a sustainer propellant together inside a metal housing. The shear strength of the bond between the two types of propellant is an important quality characteristic. It is suspected that shear strength is related to the age in weeks of the batch of sustainer propellant. Twenty observations on these two characteristics are given below. The first column is shear strength in psi (`shearpsi`

), the second is age of propellant in weeks (`agewks`

).

```
## Save the Rmd and .dat the ADA_WS_09_Data-BrainSizeData.csv data file to your computer
# this file uses spaces as delimiters, so use read.table()
rocket <- read.table("ADA1_WS_09_Data-RocketPropellant.dat", header = TRUE)
str(rocket)
```

```
## 'data.frame': 20 obs. of 2 variables:
## $ shearpsi: num 2159 1678 2316 2061 2208 ...
## $ agewks : num 15.5 23.8 8 17 5.5 ...
```

`head(rocket)`

```
## shearpsi agewks
## 1 2158.70 15.50
## 2 1678.15 23.75
## 3 2316.00 8.00
## 4 2061.30 17.00
## 5 2207.50 5.50
## 6 1708.30 19.00
```

```
library(ggplot2)
p <- ggplot(rocket, aes(x = agewks, y = shearpsi))
p <- p + geom_point()
p <- p + geom_smooth(method = lm, se = FALSE, fullrange = TRUE)
p <- p + xlim(0,NA)
print(p)
```

```
# fit the simple linear regression model
lm.shearpsi.agewks <- lm(shearpsi ~ agewks, data = rocket)
# use summary() to parameters estimates (slope, intercept) and other summaries
summary(lm.shearpsi.agewks)
```

```
##
## Call:
## lm(formula = shearpsi ~ agewks, data = rocket)
##
## Residuals:
## Min 1Q Median 3Q Max
## -215.98 -50.68 28.74 66.61 106.76
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2627.822 44.184 59.48 < 2e-16 ***
## agewks -37.154 2.889 -12.86 1.64e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 96.11 on 18 degrees of freedom
## Multiple R-squared: 0.9018, Adjusted R-squared: 0.8964
## F-statistic: 165.4 on 1 and 18 DF, p-value: 1.643e-10
```