Step 2: Simple Regression The tab called \"Simple Regression\" contains two tabl

Question

Step 2: Simple Regression The tab called "Simple Regression" contains two tables. The first is a set of data along with some regression predictions that depend on the values found in the table called "Your Model". Here is the breakdown of the data in the first table Obs. is the observation number. It runs from 1 to 10. X is the set of values for an independent variable being used to predict the dependent variable. Y is the set of values for the dependent variable being predicted by the regression. Y-hat is the set of predicted values found by multiplying X by the coefficient for 1 and then adding the value for 2. This is what the regression line predicts for Y for a given value of X. e is the set of residuals for the regression. It is the difference between Y and Y-hat. e is the residuals squared. That simple. Investigate the table of data and familiarize yourself with the equations used to calculate the regression predictions. Then start entering different values for 1 and 2 in the "Your Model" table. You'll notice things change when you do this. "Sum of Error" adds up the values of column F in the data table. "SSE" adds up the values in column G in the data table, and is otherwise known as the "Sum of Squares Error". Below this is the SSX or "Sum of Squares for X" which you will need to calculate the S.E. of the Estimate, or "Standard Error of the Estimate" below. And in the last row, you have to calculate the SE. of 1 or the "Standard Error of the Slope".

Explanation / Answer

The analysis is carried out in Excel and the output is shared below:

SUMMARY OUTPUT Regression Statistics Multiple R 0.982520448 R Square 0.96534643 Adjusted R Square 0.96039592 Standard Error 3.105413583 Observations 9 ANOVA df SS MS F Significance F Regression 1 1880.494845 1880.494845 194.9993891 2.28554E-06 Residual 7 67.50515464 9.64359352 Total 8 1948 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3.268041237 2.938169306 1.112271247 0.302755717 -3.67962516 10.21570763 -3.67962516 10.21570763 5 3.113402062 0.222955702 13.96421817 2.28554E-06 2.586195602 3.640608521 2.586195602 3.640608521 RESIDUAL OUTPUT PROBABILITY OUTPUT Observation Predicted 23 Residuals Standard Residuals Percentile 23 1 18.83505155 -2.835051546 -0.975972285 5.555555556 16 2 21.94845361 3.051546392 1.050501077 16.66666667 25 3 28.17525773 -0.175257732 -0.060332832 27.77777778 28 4 46.8556701 4.144329897 1.42669403 38.88888889 37 5 40.62886598 -3.628865979 -1.249244524 50 51 6 49.96907216 1.030927835 0.354899013 61.11111111 51 7 53.08247423 -2.082474227 -0.716896005 72.22222222 51 8 53.08247423 2.917525773 1.004364206 83.33333333 56 9 62.42268041 -2.422680412 -0.834012679 94.44444444 60

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.