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Sum of Squared Errors
Sum of Squared Errors (SSE) is calculated by squaring each residual, and then adding all of the squared residuals. We square the residuals to make them all positive, so that positive and negative residuals won't cancel each other out.
The smaller SSE is, the better the line fits the data, because this means there is a smaller total amount of error.
The least squares regression line (which is the line calculated when you find a regression line in a computer or calculator) is the line with the smallest possible SSE. It is the best line of fit for the data.
See textbook pages 123 to 124. But don't worry about doing the calculations! For this course we are only interested in the basic concept of SSE and the least squares line.
Correlation
Correlation is the strength of a linear trend.
The correlation is represented by the letter r. Correlation can range from -1 to +1.
The closer r is to 1 or -1, the stronger the trend. The closer to 0, the weaker the trend.
See page 140 as a guide, then answer questions P9 on page 155 and E27on page 158. After you complete the questions, check your answers in the back of the book.
Correlation does not imply causation.
A strong correlation between two variables tells you that there is a relationship between the variables. However, this does not necessarily mean that there is a cause and effect relationship between the variables. In other words, it does not mean that changes in one variable explain WHY the other variable is changing. Often there is a lurking, or hidden, variable that can explain both of the other variables.
For example, there is a strong positive trend between ice cream sales and number of shark attacks. However, ice cream does NOT cause sharks to attack people. The real explanation is a lurking variable: the weather. When it is warm out, people buy ice cream. When it is warm out, people go into the water, where they might get attacked. The weather is a hidden factor that explains why ice cream sales and shark attacks seem to have a relationship.
See textbook page 147. Then answer questions P17 and P18 on page 157. After you complete the questions, check your answers in the back of the book.