Do tall people generally have larger feet than short people? Use the data below to answer the ff. Shoe Size Height (inches) Gender Shoe Size Height (inches) Gender 6.5 66.0 F 13.0 77.0 M 9.0 68.0 F 11.5 72.0 M 8.5 64.5 F 8.5 59.0 F 8.5 65.0 M 5.0 62.0 F 10.5 70.0 M 10.0 72.0 M 7.0 64.0 F 6.5 66.0 F 9.5 70.0 F 7.5 64.0 F 9.0 71.0 M 8.5 67.0 M 13.0 72.0 M 10.5 73.0 M 7.5 64.0 F 8.5 69.0 F 10.5 74.5 M 10.5 72.0 M 8.5 67.0 F 11.0 70.0 M 12.0 71.0 M 9.0 69.0 M 10.5 71.0 M 13.0 70.0 M Find the regression equation for the data, using shoe size as the predictor variable. Interpret the slope of the regression line. Use the regression equation to predict the height of a male student who wears a size 10 ½ shoe.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Do tall people generally have larger feet than short people? Use the data below to answer the ff.
|
Shoe Size |
Height (inches) |
Gender |
Shoe Size |
Height (inches) |
Gender |
|
6.5 |
66.0 |
F |
13.0 |
77.0 |
M |
|
9.0 |
68.0 |
F |
11.5 |
72.0 |
M |
|
8.5 |
64.5 |
F |
8.5 |
59.0 |
F |
|
8.5 |
65.0 |
M |
5.0 |
62.0 |
F |
|
10.5 |
70.0 |
M |
10.0 |
72.0 |
M |
|
7.0 |
64.0 |
F |
6.5 |
66.0 |
F |
|
9.5 |
70.0 |
F |
7.5 |
64.0 |
F |
|
9.0 |
71.0 |
M |
8.5 |
67.0 |
M |
|
13.0 |
72.0 |
M |
10.5 |
73.0 |
M |
|
7.5 |
64.0 |
F |
8.5 |
69.0 |
F |
|
10.5 |
74.5 |
M |
10.5 |
72.0 |
M |
|
8.5 |
67.0 |
F |
11.0 |
70.0 |
M |
|
12.0 |
71.0 |
M |
9.0 |
69.0 |
M |
|
10.5 |
71.0 |
M |
13.0 |
70.0 |
M |
- Find the regression equation for the data, using shoe size as the predictor variable.
- Interpret the slope of the regression line.
- Use the regression equation to predict the height of a male student who wears a size 10 ½ shoe.
- Obtain and interpret the coefficient of determination.
- Compute the
correlation coefficient of the data, and interpret your result. - Identify outliers and potential influential observations, if any.
- If there are outliers, first remove them, and then repeat parts (b)-('h).
- Decide whether any potential influential observation that you detected is in fact an influential observation. Explain your reasoning.
- Repeat parts (b)–(k) for the data on shoe size and height for females. For part (f), do the prediction for the height of a female student who wears a size 8 shoe.
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