Please download the answer file and edit it on *RStudio*. Write your student number in the correct place at the beginning of the answer file. When you finish, send the `answers.R`

file to the answers’ mailbox. All questions are independent and can be answered in any order.

# Papers published by our University

The database *PubMed* contains a catalog of all papers published by our university in *international journals of biological sciences*. The following code will create a data frame with the number of publications for each year. If you *knit* the document, it will be automatically included. Do not delete it, do not duplicate it.

```
pubmed <- data.frame(year = c(2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011,
2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999, 1998,
1997, 1996, 1995, 1994, 1993, 1992, 1991, 1990, 1989, 1988, 1987, 1986, 1975,
1974, 1965, 1940), number = c(1001, 1194, 1328, 1154, 942, 681, 618, 534, 506,
510, 468, 524, 495, 493, 477, 400, 265, 168, 141, 127, 93, 74, 68, 61, 34, 43,
23, 14, 13, 10, 8, 2, 3, 2, 1, 1, 2))
```

## Write an R command to plot the number of papers depending on the year

`# write your answer here`

## Write an R command to build a linear model to predict the number of papers depending on the year. Assign the model to the variable `model`

and show it

`# write your answer here`

```
##
## Call:
## lm(formula = log(number) ~ year, data = pubmed, subset = year >
## 1980 & year < 2016)
##
## Coefficients:
## (Intercept) year
## -386.2718 0.1955
```

## Write an R command to plot the number of papers depending on the year, and the line of values predicted by `model`

. Notice that we *do not* plot logarithms, but we use a logarithmic scale

`# write your answer here`

## Write the code to print the growth rate (percentage) for each year. This growth rate is calculated from the values of the coefficients of the model.

`# write your answer here`

```
## year
## 21.58631
```

# Circles

## We want to draw circles, ellipses and spirals. Please create a vector `t`

with numbers from `0`

to `2*pi`

in steps of `0.1`

. Then draw this graphic with `cos(t)`

on the horizontal axis, and `sin(t)`

in the vertical axis

## Now draw the same circle but with the symbol size proportional to `1-cos(t)`

## This time the radius should change with `t`

. Please draw this graphic with `t*cos(2*t)`

on the horizontal and `t*sin(2*t)`

in the vertical axis

# Kepler’s Law

For this question you must use the data frame defined by the following code.

```
planets <- data.frame(Name = c("Mercury", "Venus", "Earth", "Mars", "Jupiter",
"Saturn", "Uranus", "Neptune"), Diameter = c(4879, 12104, 12742, 6779, 139822,
116464, 50724, 49244), Distance = c(57909227, 108209475, 149598262, 227943824,
778340821, 1426666422, 2870658186, 4498396441), Period = c(88, 225, 365.24,
687, 4346.356, 10774.58, 30680.16, 60191.552))
```

## Draw three plots: normal, semi-log and log-log scales. Each plot must have *Distance* in the horizontal axis, *Period* in the vertical axis, and the symbol size must be proportional to *Diameter/50000*.

`# write your answer here`

## Based on the 3 plots, decide which is the best approach to use a linear model. Build the model and show the coefficients

`# write your answer here`

```
## (Intercept) log(Distance)
## -22.331471 1.499873
```

## (bonus) Compare your result with *Kepler’s third law*

`# write your answer here`