Question 2 [50 points] MATH 208 Final Exam Solution

Description

We will re-use the same midwest_modified data that was used in Question 1, with all the modifications from the other question parts. The description is repeated below for your convenience.

str(midwest_modified)

spec_tbl_df [437 x 11] (S3: spec_tbl_df/tbl_df/tbl/data.frame)

$ county	: chr [1:437]	“ADAMS” “ALEXANDER” “BOND” “BOONE” …
$ state	: chr [1:437]	“IL” “IL” “IL” “IL” …
$ popdensity	: num [1:437]	1271 759 681 1812 324 …
$ popwhite	: num [1:437]	63917 7054 14477 29344 5264 …
$ popblack	: num [1:437]	1702 3496 429 127 547 …
$ popamerindian: num [1:437]		98 19 35 46 14 65 8 30 8 331 …
$ popasian	: num [1:437]	249	48 16 150 5 …
$ popother	: num [1:437]	124	9 34 1139 6 …
$ inmetro	: num [1:437]	0 0	01000001…
$ Metro	: chr [1:437]	“NonMetro” “NonMetro” “NonMetro” “Metro” …
$ HighDens	: chr [1:437]	“NotHigh” “NotHigh” “NotHigh” “High” …

• attr(*, “spec”)=

.. cols(

.. county = col_character(),

.. state = col_character(),

.. popdensity = col_double(),

.. popwhite = col_double(),

.. popblack = col_double(),

.. popamerindian = col_double(),

.. popasian = col_double(),

.. popother = col_double(),

.. inmetro = col_double(),

.. Metro = col_character(),

.. HighDens = col_character()

.. )

midwest_modified %>% slice(1:5) %>%

select(county:popblack)

# A tibble:		5 x 5
	county	state popdensity popwhite popblack
	<chr>	<chr>	<dbl>	<dbl>	<dbl>
1	ADAMS	IL	1271.	63917	1702
2	ALEXANDER	IL	759	7054	3496
3	BOND	IL	681.	14477	429
4	BOONE	IL	1812.	29344	127
5	BROWN	IL	324.	5264	547
midwest_modified %>% slice(1:5) %>%
	select(county,popamerindian:HighDens)
# A tibble:		5 x 7
	county	popamerindian popasian popother inmetro Metro						HighDens
	<chr>		<dbl>	<dbl>	<dbl>	<dbl> <chr>		<chr>
1	ADAMS		98	249	124	0	NonMetro	NotHigh
2	ALEXANDER		19	48	9	0	NonMetro	NotHigh
3	BOND		35	16	34	0	NonMetro	NotHigh
4	BOONE		46	150	1139	1	Metro	High
5	BROWN		14	5	6	0	NonMetro	NotHigh

The dataset contains population data from midwest counties in five states in the United States from an unspecified year. There are identifying variables for both the county (the name) and the state (the postal abbreviation).

MATH 208 Final Exam December 18th – 21st,

The variable popdensity is a measure of density (population per unspecified area units). The variable inmetro is equal to 1 if the county is classified as a metropolitan area and 0 otherwise. The other variables contain counts of population size within self-identified racial classifications.

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MATH 208 Final Exam December 18th – 21st,

1. [6 pts] Below are partially obscured code and three plots of the values of the log (base 10) of the population density for all counties:

p1<-ggplot(midwest_modified,aes(x=popdensity)) + geom_XXXXX(nbins=30,fill=“white”,col=“black”) + ggtitle(“Plot 1”) + theme_bw() + scale_x_log10()

p2<-ggplot(midwest_modified,aes(x=popdensity)) + geom_YYYYY() + ggtitle(“Plot 2”) + theme_bw()+ scale_x_log10()

p3<-ggplot(midwest_modified,aes(x=popdensity)) + geom_ZZZZZ() + ggtitle(“Plot 3”) + theme_bw()+ scale_x_log10()

grid.arrange(grobs=list(p1,p2,p3),nrow=3,ncol=1)

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Plot 1

	60
count	40
	20
	0
	1e+02	1e+03	1e+04	1e+05
			popdensity

Plot 2

MATH 208 Final Exam December 18th – 21st,

Plot 1

	20
	15
	10			IL
	5
	0
	20
	15			IN
	10
	5
	0
	20
count	15			MI
	10
	5
	0
	20
	15			OH
	10
	5
	0
	20
	15			WI
	10
	5
	0
	1e+02	1e+03	1e+04	1e+05
		popdensity
grid.arrange(grobs=list(p2,p3),nrow=2,ncol=1)

	Plot 2
				state
	1.0			IL
density				MI
	0.5
				IN
				OH
	0.0			WI
	1e+02	1e+03	1e+04	1e+05
			popdensity

Plot 3

MATH 208 Final Exam December 18th – 21st,

3. [4 pts] Which plot(s) do you think best shows the association between state and population density? Which plot(s) do you think does not shows the association between state and population density as clearly? Explain your answer and reasoning in a few sentences.

3. [5 pts] Which of the following plots could also be used to assess the association between the popwhite and popblack variables? List all that apply (or say None if none would be appropriate).

A. 2-d density plot B. Barplot C. Boxplot D. 2-d histogram

We now would like to make plots to take a different look at the population variables. Unfortunately, the format of the midwest_modified data needs to be further changed so that we can use it in a ggplot.

5. [5 pts] Write a line of code that will create a new tibble converts the midwest_modified_new to “long” format where each row contains a population count for a specific racial group called Count, and the variable from where that count originated (e.g. popwhite) as well as the state, county, and Metro information for that population group. You should not include the columns for HighDens, inmetro or popdensity. The first 10 rows of the new tibble are below

midwest_modified_new %>% slice(1:10)

# A tibble: 10 x 5
	county	state Metro		Race_Variable Count
	<chr>	<chr> <chr>		<chr>	<dbl>
1	ADAMS	IL	NonMetro	popwhite	63917
2	ADAMS	IL	NonMetro	popblack	1702
3	ADAMS	IL	NonMetro	popamerindian	98
4	ADAMS	IL	NonMetro	popasian	249
5	ADAMS	IL	NonMetro	popother	124
6	ALEXANDER	IL	NonMetro	popwhite	7054
7	ALEXANDER	IL	NonMetro	popblack	3496
8	ALEXANDER	IL	NonMetro	popamerindian	19
9	ALEXANDER	IL	NonMetro	popasian	48
10	ALEXANDER	IL	NonMetro	popother	9

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MATH 208 Final Exam December 18th – 21st,

(h) [5 pts] Using the tibble from (g), write a line of code that created the barplot below.

7