R Assignment 4 - Kevin Pham
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Montgomery College *
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Statistics
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Feb 20, 2024
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docx
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Kevin Pham
STAT100 Section 0331
R Assignment 4
1.a. The explanatory variable is the Server variable.
1.b. The response variable is the Pct_Tip variable.
1.c. The role-type classification is C->Q
1.d.
Boxplot of Server and Pct_Tip variables with default formatting settings:
Boxplot of Server and Pct_Tip variables with customized formatting settings:
1.e. The server that had the highest median tip percentage was Ashley at 16.75.
1.f. The server that had the least median tip percentage was Byron at 15.60. 1.g. The box plots show that median tip percentage for Ashley was 16.75, Byron was 15.60, and Cassandra was 16.25 which around 15-16%. These results show that every server received at least 13% in tips and no more than 20%. The average for every server is around 16-17%. Based on these small differences between the servers and tip percentages, there is little to no relationship between the two variables. 2.a. The explanatory variable is the Bill variable. 2.b.
The response variable is the Pct_Tip variable. 2.c.
The role-type classification is Q->Q. 2.d.
Scatterplot of Bill and Pct_Tip variables with default formatting settings:
Scatterplot of Bill and Pct_Tip variables with customized formatting settings:
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2.e. The correlation coefficient for this potential relationship is r = 0.1353. 2.f. The value of the correlation coefficient indicates that there is a weak positive linear relationship between the bill amount and tip percentage. 2.g.
The least-squares linear regression equation for this relationship is Tip Percentage = 15.50965 - 0.04881 (Bill). 2.h.
Tip Percentage = 15.50965 - 0.04881 (Bill)
= 15.50965 - 0.04881 (50)
= 15.50965 - 2.4405
= 13.07%
The tip percentage is 13.07% for a table with a total bill of $50.00.
2.i. The scatterplot seems to indicate a weak positive relationship between the bill and tip percentage. There is no strong linear shape present in the scatterplot based on how spread out the
points are. The correlation coefficient r = 0.1353 can be interpreted as a weak positive relationship because of how close it is to zero. The regression equation also reveals that for every
dollar of the bill, we would expect 0.1353 percent to be charged for the tip percentage. The value
of the slope is very close to zero which means there is a weak positive relationship between the bill and the tip percentage.
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