A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain. MPG HORSEPOWER WEIGHT 44 67 1,844 44 50 1,998 40 62 1,752 37 69 1,980 37 66 1,797 34 63 2,199 35 90 2,404 32 99 2,611 30 63 3,236 28 91 2,606 26 94 2,580 26 88 2,507 25 124 2,922 22 97 2,434 20 114 3,248 21 102 2,812 18 114 3,382 18 142 3,197 16 153 4,380 16 139 4,036
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.
A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were recorded. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain.
|
MPG |
HORSEPOWER |
WEIGHT |
|
44 |
67 |
1,844 |
|
44 |
50 |
1,998 |
|
40 |
62 |
1,752 |
|
37 |
69 |
1,980 |
|
37 |
66 |
1,797 |
|
34 |
63 |
2,199 |
|
35 |
90 |
2,404 |
|
32 |
99 |
2,611 |
|
30 |
63 |
3,236 |
|
28 |
91 |
2,606 |
|
26 |
94 |
2,580 |
|
26 |
88 |
2,507 |
|
25 |
124 |
2,922 |
|
22 |
97 |
2,434 |
|
20 |
114 |
3,248 |
|
21 |
102 |
2,812 |
|
18 |
114 |
3,382 |
|
18 |
142 |
3,197 |
|
16 |
153 |
4,380 |
|
16 |
139 |
4,036 |
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