Bivariate regression and correlation measures

Bivariate regression and correlation measures

1. Correlation

   • is to measure the closeness of the relationship between two or more variables.
     • The sign of correlation is (+ or -), we have the linear correlation which expresses the linear strength and direction: - the perfect negative which is -1 - the strong negative - 1a -0.95 - the moderate negative which is -0.95 to -0.05 - the weak negative is from - 0.5 to - 0.1 and so on up to 0 - weak positive is 0.1 to 0.5 - moderate positive is 0.5 to 0.95 - strong is from 0.95 to one - perfect is 1
       • NOTE: The closer the linear relationship is to zero, the weaker it is, and in the negative correlation, one variable falls while the other increases.

2. Objectives

   • to measure the relationship between two or more variables such as income, production, hours worked and consumption.

3. Correlation coefficient

   • this quantifies the intensity of the linear relationship between two variables is symbolized with the r and it compares the distance of the data as such according to the variable and the result of this will show us how much relationship exists between them. Characteristics: does not detect outliers or outliers and does not correctly detect curvilinear relationships.
     • Example: if we want to know what the purchase of soda depends on, if it can be because of the heat or because of what people like to drink, for that we must calculate the relationship and for this: 1. we have a variable of average daily sales of coca-cola soda and the second variable is the maximum daily temperature. 2. we make a scatter diagram with the data.
     • 3. We subtract the measurement from the daily sale
     • 4. the even values are located, then multiplied and this result is added up [(-4) (-5) + (0) (0) + (4) (5)] = 40 5. we determine the denominator of the equation, for this we add the expressions separately to the square and this sum we are going to multiply it and then we take out the square root so we find the denominator of the equation
       • 6. finally we complete the calculation and compare the result with the scatter plot giving us a perfect correlation between sales of coca-cola soda and the days when it is hot, which means that the temperature affects the sales of coca-cola soda and not so much because people like to drink it, but because they like to drink it.

4. regression

   • needs a mathematical equation to write that relationship.

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