d) Find the slope, the intercept and the regression equation. e) Find the best predicted height of a person that has a shoe print of 29cm. f) According to the regression equation. For each increment of 1cm in shoe print, what is the increment that we should expect in height? Data SEX AGE FOOT LENGTH SHOE PRINT SHOE SIZE HEIGHT M 67 27.8 31.3 11 180.3 M 47 25.7 29.7 9 175.3 M 41 26.7 31.3 11 184.8 M 42 25.9 31.8 10 177.8 M 48 26.4 31.4 10 182.3 M 34 29.2 31.9 13 185.4 M 26 26.8 31.8 11 180.3 M 29 28.1 31 10.5 175.3 M 60 25.4 29.7 9.5 177.8 M 48 27.9 31.4 11 185.4 M 30 27.5 31.4 11 190.5 M 43 28.8 31.6 12 195 M 54 26.7 31.8 10 175.3 M 31 26.7 32.4 10.5 180.3 M 42 25.1 27.6 9 172.7 M 21 28.7 31.8 12.5 182.9 M 59 29.2 31.3 11 189.2 M 58 27.9 31.3 11.5 185.4 M 42 28.6 34.5 14 193.7 F 47 23.2 24.8 7 165.1 F 19 24.3 28.6 9 166.4 F 20 26 25.4 10 177.8 F 27 23.8 26.7 8 167.6 F 19 25.1 26.7 9 168.3 F 21 25.4 27.9 8.5 165.7 F 32 21.9 27.9 8 165.1 F 19 26.2 28.9 11 165.1 F 27 23.8 27.9 8 165.1 F 18 22.2 25.9 9.5 152.4 F 26 24.6 25.4 8.5 162.6 F 36 24.6 28.1 9 179.1 F 28 23.7 27.6 9 175.9 F 29 25.6 26.5 8.5 166.4 F 58 24.1 26.5 7 167.6 F 30 23.8 28.4 9 162.6 F 23 23.3 26.5 8 167.6 F 26 23.5 26 8 165.1 F 47 25.1 27 10 172.7 F 36 24.1 25.1 7.5 157.5 F 19 23.8 27.9 10 167.6
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.
d) Find the slope, the intercept and the regression equation.
e) Find the best predicted height of a person that has a shoe print of 29cm.
f) According to the regression equation. For each increment of 1cm in shoe print, what is the increment that we should expect in height?
Data
| SEX | AGE | FOOT LENGTH | SHOE PRINT | SHOE SIZE | HEIGHT |
| M | 67 | 27.8 | 31.3 | 11 | 180.3 |
| M | 47 | 25.7 | 29.7 | 9 | 175.3 |
| M | 41 | 26.7 | 31.3 | 11 | 184.8 |
| M | 42 | 25.9 | 31.8 | 10 | 177.8 |
| M | 48 | 26.4 | 31.4 | 10 | 182.3 |
| M | 34 | 29.2 | 31.9 | 13 | 185.4 |
| M | 26 | 26.8 | 31.8 | 11 | 180.3 |
| M | 29 | 28.1 | 31 | 10.5 | 175.3 |
| M | 60 | 25.4 | 29.7 | 9.5 | 177.8 |
| M | 48 | 27.9 | 31.4 | 11 | 185.4 |
| M | 30 | 27.5 | 31.4 | 11 | 190.5 |
| M | 43 | 28.8 | 31.6 | 12 | 195 |
| M | 54 | 26.7 | 31.8 | 10 | 175.3 |
| M | 31 | 26.7 | 32.4 | 10.5 | 180.3 |
| M | 42 | 25.1 | 27.6 | 9 | 172.7 |
| M | 21 | 28.7 | 31.8 | 12.5 | 182.9 |
| M | 59 | 29.2 | 31.3 | 11 | 189.2 |
| M | 58 | 27.9 | 31.3 | 11.5 | 185.4 |
| M | 42 | 28.6 | 34.5 | 14 | 193.7 |
| F | 47 | 23.2 | 24.8 | 7 | 165.1 |
| F | 19 | 24.3 | 28.6 | 9 | 166.4 |
| F | 20 | 26 | 25.4 | 10 | 177.8 |
| F | 27 | 23.8 | 26.7 | 8 | 167.6 |
| F | 19 | 25.1 | 26.7 | 9 | 168.3 |
| F | 21 | 25.4 | 27.9 | 8.5 | 165.7 |
| F | 32 | 21.9 | 27.9 | 8 | 165.1 |
| F | 19 | 26.2 | 28.9 | 11 | 165.1 |
| F | 27 | 23.8 | 27.9 | 8 | 165.1 |
| F | 18 | 22.2 | 25.9 | 9.5 | 152.4 |
| F | 26 | 24.6 | 25.4 | 8.5 | 162.6 |
| F | 36 | 24.6 | 28.1 | 9 | 179.1 |
| F | 28 | 23.7 | 27.6 | 9 | 175.9 |
| F | 29 | 25.6 | 26.5 | 8.5 | 166.4 |
| F | 58 | 24.1 | 26.5 | 7 | 167.6 |
| F | 30 | 23.8 | 28.4 | 9 | 162.6 |
| F | 23 | 23.3 | 26.5 | 8 | 167.6 |
| F | 26 | 23.5 | 26 | 8 | 165.1 |
| F | 47 | 25.1 | 27 | 10 | 172.7 |
| F | 36 | 24.1 | 25.1 | 7.5 | 157.5 |
| F | 19 | 23.8 | 27.9 | 10 | 167.6 |
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