Question

review
use the table to make a scatter plot of the number of hours participating in clubs and the number of hours participating in sports. describe the correlation between the two.
hours spent on activities over one week

• positive correlation: two data sets generally increase together
• negative correlation: one data set generally increases while the other decreases
• no correlation: no apparent trend or relationship between two data sets

step 1 make a scatterplot.
plot each ordered pair (clubs, sports) using the data from the table. the scatterplot has been started at the right. please complete it.
step 2 analyze the trend of the data.
as the number of hours participating in clubs increases, the number of hours participating in sports________(increases / decreases / does not show a trend). thus, there is________(a positive / a negative / no) correlation between the data sets.
practice make a scatter plot for the given data sets using the table above. describe the correlation between each set.

1. (clubs, apps + tv)
2. (sports, apps + tv)
3. (apps, tv)
4. (clubs + sports, apps + tv)

Explanation:

Step1: Analyze the data for (clubs, apps + TV)

For Cecil: clubs = 1, apps + TV=16 + 9=25
For Latoya: clubs = 1, apps + TV=4 + 6=10
For Lily: clubs = 2, apps + TV=0 + 11=11
For Chris: clubs = 3, apps + TV=9 + 8=17
For Liam: clubs = 2, apps + TV=14 + 5=19
For Erica: clubs = 0, apps + TV=0 + 3=3
For Edward: clubs = 0, apps + TV=5 + 4=9
As the number of hours in clubs increases, the value of apps + TV does not follow a consistent increasing or decreasing trend.

Step2: Analyze the data for (sports, apps + TV)

For Cecil: sports = 0, apps + TV=25
For Latoya: sports = 14, apps + TV=10
For Lily: sports = 10, apps + TV=11
For Chris: sports = 0, apps + TV=17
For Liam: sports = 0, apps + TV=19
For Erica: sports = 8, apps + TV=3
For Edward: sports = 15, apps + TV=9
As sports hours increase, apps + TV hours do not show a clear increasing or decreasing trend.

Step3: Analyze the data for (apps, TV)

For Cecil: apps = 16, TV = 9
For Latoya: apps = 4, TV = 6
For Lily: apps = 0, TV = 11
For Chris: apps = 9, TV = 8
For Liam: apps = 14, TV = 5
For Erica: apps = 0, TV = 3
For Edward: apps = 5, TV = 4
There is no clear pattern where as apps hours increase, TV hours consistently increase or decrease.

Step4: Analyze the data for (clubs + sports, apps + TV)

Clubs + sports:
Cecil:1 + 0=1; Latoya:1 + 14=15; Lily:2 + 10=12; Chris:3+0 = 3; Liam:2 + 0=2; Erica:0 + 8=8; Edward:0+15 = 15
Apps + TV:
Cecil:25; Latoya:10; Lily:11; Chris:17; Liam:19; Erica:3; Edward:9
As (clubs + sports) hours increase, apps + TV hours do not show a consistent increasing or decreasing trend.

Answer:

1. For (clubs, apps + TV): As the number of hours participating in clubs increases, the number of hours (apps + TV) does not show a trend. Thus, there is no correlation.
2. For (sports, apps + TV): As the number of hours participating in sports increases, the number of hours (apps + TV) does not show a trend. Thus, there is no correlation.
3. For (apps, TV): As the number of hours using apps increases, the number of hours watching TV does not show a trend. Thus, there is no correlation.
4. For (clubs + sports, apps + TV): As the number of hours (clubs + sports) increases, the number of hours (apps + TV) does not show a trend. Thus, there is no correlation.