Pre-test: Regression with Orange Data Mining

Use this Excel file to answer all the questions.

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workflow with Orange Data Mining

1. How many observations in this data set?

Answer:

2. Pearson Correlation

   2.1) The Pearson Correlation between \(y\) and \(x1\)

   2.2) The Pearson Correlation between \(y\) and \(x2\)

   2.3) The Pearson Correlation between \(y\) and \(x3\)

   2.4) The Pearson Correlation between \(x1\) and \(x2\)

   2.5) The Pearson Correlation between \(x1\) and \(x3\)

   2.6) The Pearson Correlation between \(x2\) and \(x3\)

3. If we choose the simple linear regression.

\[y =a+bx_1 + \varepsilon\] What are the values of \(a\), \(b\) and R2 (R-squared)?

\(a\) = \(b\) = \(R2\) =

4. If we choose the simple linear regression.

\[y =a+b x_2 + \varepsilon\] What are the values of \(a\), \(b\) and R2 (R-squared)?

\(a\) = \(b\) = \(R2\) =

5. If we choose the simple linear regression.

\[y =a+b x_1 + cx_2+\varepsilon\] What are the values of \(a\), \(b\), \(c\) and R2 (R-squared)?

\(a\) = \(b\) = \(c\) = \(R2\) =

6. If we choose the simple linear regression.

\[y =a+b x_1 + cx_2+dx_3+\varepsilon\]

What are the values of \(a\), \(b\), \(c\), \(d\) and R2 (R-squared)?

\(a\) = \(b\) = \(c\) = \(d\) = \(R2\) =

7. Predict \(y\) using the regression from question 6.

Use this Excel file to predict the value.

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Linear Regression	x1	x2	x3
	7.02	13.46	16.46
	1.37	18.83	30.31
	5.49	14.89	15.93
	7.20	22.46	19.87
	8.77	17.24	24.30