Final answer:
In the Mpg.csv dataset, the independent variable could be the size of the car's engine, and the dependent variable could be the miles per gallon (MPG) of the car.
To determine the importance of variables against the training set, a basic linear regression can be performed, along with creating a scatter plot to visualize the relationship between the variables. The correlation coefficient can provide further information about the strength and significance of the relationship.
Step-by-step explanation:
a. The independent variable is the variable that is manipulated or controlled in an experiment, and the dependent variable is the variable that is measured or observed. In the Mpg.csv dataset, the independent variable could be the size of the car's engine, and the dependent variable could be the miles per gallon (MPG) of the car.
b. To draw a scatter plot of the data, you can plot the independent variable (size of the engine) on the x-axis and the dependent variable (MPG) on the y-axis. Each data point represents a car's engine size and its corresponding MPG.
c. Using regression, you can find the line of best fit that represents the relationship between the independent and dependent variables. The correlation coefficient is a measure of the strength and direction of the linear relationship between the variables.
d. The significance of the correlation coefficient indicates how strongly the independent and dependent variables are related. A correlation coefficient close to +1 or -1 indicates a strong linear relationship, while a correlation coefficient close to 0 indicates a weak or no linear relationship.
e. To determine if there is a linear relationship between the variables, you can examine the scatter plot and observe if the points roughly follow a straight line pattern. Additionally, calculating the correlation coefficient can provide quantitative evidence of a linear relationship.