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Chapter 13: Problem 9

Explain the meaning and concept of SSE. You may use a graph for illustration purposes.

Short Answer

Expert verified
Sum of Squared Errors (SSE) is a measure of the discrepancy between data and an estimation model. It is primarily used as a quality measure for statistical estimations and regression models. The lower the SSE, the better the model's predictive power. In a graphical representation, SSE is calculated by summing the squared vertical distances of all data points from the estimated line on a scatter plot.

Step by step solution

01

Define SSE

The Sum of Squared Errors (SSE) is a measure of the discrepancy between the data and an estimation model. A small SSE indicates a tight fit of the model to the data. It is the sum of the squared differences between the actual and the estimated values.
02

Explain the Use of SSE

SSE is primarily used as a measure of the quality of a statistical estimator or a regression model. The lower the SSE, the better the model is at predicting the data.
03

Illustrate with a Graph

To illustrate this concept, imagine a scatter plot of data points. Draw a line that you think best fits the data. For each data point, measure the vertical distance between the point and the line, square it, and sum these squared values across all data points. This sum is the SSE.

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Most popular questions from this chapter

Explain the meaning of the words simple and linear as used in simple linear regression.

Explain the least squares method and least squares regression line. Why are they called by these names?

The following table gives information on the incomes (in thousands of dollars) and charitable contributions (in hundreds of dollars) for the last year for a random sample of 10 households. $$ \begin{array}{cc} \hline \text { Income } & \text { Charitable Contributions } \\ \hline 76 & 15 \\ 57 & 4 \\ 140 & 42 \\ 97 & 33 \\ 75 & 5 \\ 107 & 32 \\ 65 & 10 \\ 77 & 18 \\ 102 & 28 \\ 53 & 4 \\ \hline \end{array} $$ a. With income as an independent variable and charitable contributions as a dependent variable, compute \(\mathrm{SS}_{x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x y}\) b. Find the regression of charitable contributions on income. c. Briefly explain the meaning of the values of \(a\) and \(b\). d. Calculate \(r\) and \(r^{2}\) and briefly explain what they mean. e. Compute the standard deviation of errors. f. Construct a 99 \% confidence interval for \(B\). g. Test at a \(1 \%\) significance level whether \(B\) is positive. h. Using a \(1 \%\) significance level, can you conclude that the linear correlation coefficient is different from zero?

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The following table gives the average weekly retail price of a gallon of regular gasoline in the eastern United States over a 9-week period from December 1, 2014, through January 26, 2015. Consider these 9 weeks as a random sample. $$ \begin{array}{l|rrrrrr} \hline \text { Date } & 12 / 1 / 14 & 12 / 8 / 14 & 12 / 15 / 14 & 12 / 22 / 14 & 12 / 29 / 14 & 1 / 5 / 15 \\ \hline \text { Price (\$) } & 2.861 & 2.776 & 2.667 & 2.535 & 2.445 & 2.378 \\\ \hline \text { Date } & 1 / 12 / 15 & 1 / 19 / 15 & 1 / 26 / 15 & & & \\ \hline \text { Price (\$) } & 2.293 & 2.204 & 2.174 & & & \\ \hline \end{array} $$ a. Assign a value of 0 to \(12 / 1 / 14,1\) to \(12 / 8 / 14,2\) to \(12 / 15 / 14\), and so on. Call this new variable Time. Make a new table with the variables Time and Price. b. With time as an independent variable and price as the dependent variable, compute \(S S_{x x}, S S_{y y}\), and \(S S_{x y}\) c. Construct a scatter diagram for these data. Does the scatter diagram exhibit a negative linear relationship between time and price? d. Find the least squares regression line \(\hat{y}=a+b x\). e. Give a brief interpretation of the values of \(a\) and \(b\) calculated in part \(\mathrm{d}\). f. Compute the correlation coefficient \(r .\) g. Predict the average price of a gallon of regular gasoline in the eastern United States for Time \(=26 .\) Comment on this prediction.
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