Question

You have been told that the amount of education a person obtains will guarantee them a high paying job. That is, their pay depends on their education. Discuss problems with this statement. Give a specific example of an individual that would be considered an outlier of this data set.

You have been asked to find if there is a correlation between the amount of calories per serving in a bowl of cereal versus the amount of sugar (in grams) in the cereal. The following data has been given for examination.

Sugar.               Calories.                                           18.                     200
23.                     210
12.                     170
12.                     190
37.                     220
19.                     175
23.                     201
22.                     210
32.                     210
11.                     190
11.                     197
29.                     205

a.   Create a scatterplot of the given data. Be sure you explain your decision on which variable is the predictor and which variable is the response.
b.   Using computer software, calculate the correlation coefficient and interpret what this value implies in relation to the data set.
c.   Create a regression equation that models the data and describe the values of the slope and y-intercept with the data set.
d.   Predict if a box of cereal has 25 grams of sugar per serving how many calories it will contain.
e.   Predict if a box of cereal has 230 calories per serving how much sugar (in grams) it will contain.
f.   Discuss any lurking variables could be relevant to analysis of this data set.

Answer 1

Solution:

with plot function in R we can get the scatterplot

using R studio

df1 =read.table(header = TRUE, text ="
Sugar Calories   
23 210
12 170
12 190
37 220
19 175
23 201
22 210
32 210
11 190
11 197
29 205
18 200

"
)
df1

plot(Calories ~ Sugar,data=df1,pch=16)

210 Calories 190 170 10 15 20 25 30 35 Sugar

From scatterplot we get

Form:linear

strength:strong

direction:positive

b.   Using computer software, calculate the correlation coefficient and interpret what this value implies in relation to the data set.

use cor fucntion to get the correlation coefficient

cor(df1$Sugar,df1$Calories)

Output:

0.7339425

r=0.7339425

There exists a strong positive relatonship between sugar and calries

as amount of sugar (in grams) in the cereal. increases, amount of calories per serving in a bowl increases

c.   Create a regression equation that models the data and describe the values of the slope and y-intercept with the data set.

Rcode:
linmod <- lm(Calories ~ Sugar,data=df1)
coefficients(linmod)

output:

Intercept) Sugar
172.073400 1.257507

regression equation is

calories= 172.073400 + 1.257507 *sugar

slope=1.257507

y intercept=172.073400

d.   Predict if a box of cereal has 25 grams of sugar per serving how many calories it will contain.

calories= 172.073400 + 1.257507 *sugar

we have sugar=25

calories= 172.073400 + 1.257507 *25

=203.5111

predicted calories=203.5111 for a  cereal that  has 25 grams of sugar