# Regression Analysis Practice

Regression Analysis Practice

Project description
Step 2
Make sure you have the Data Analysis ToolPak add-in for your Excel. You can do that by going to the Data tab and searching for Data Analysis. If it does not appear, you will need to download it. The steps to download add-ins varies with each version of Excel. Here are the steps for the 2007 version:

Click on the Excel icon in the upper-left corner of your spreadsheet.
Click on Excel Options.
Along the left-side menu, click on Add-Ins.
Select Analysis ToolPak and follow the instructions.

*For Mac users, StatPlus is the recommended free program

Step 3
At the bottom, click on the Demand for Jet Fuel tab. The sample demand equation is estimated using this data set, and the results are shown. For your submission you will be using the Gasoline data on the adjacent tab.

Step 4
Use the procedure described to estimate the demand for gasoline using the same steps identified in the example below. Sample answers are based on the Demand for Jet Fuel data.

1.Evaluate adjusted R2.
The adjusted R2 is 0.778421. It indicates that approximately 78% of the variation in the demand for jet fuel across states is explained by the three independent variablesprice, state GDP, and state population.

2.Evaluate each of the independent variables using a t-test.
Table 1 provides the results of the t-tests for each of the independent variables.

CoefficientsStandard ErrorT-StatP-Value
Intercept-18.449845.28617-0.407410.68556
Price0.1384292.7885820.0496410.960619
GDP0.1700790.0391654.3426467.45E-05
Population0.0052810.0017912.9480360.004967
Table 1: T-Test Analysis

To assist use the Student t-Value Calculator: http://www.danielsoper.com/statcalc3/calc.aspx?id=10
The degrees of freedom are 47, and the probability is 0.05. The critical value is approximately 2. If the absolute value of the t-statistic is greater than 2, the null hypothesis can be rejected. The P-value results can be used to determine whether to reject each of the following hypotheses.

*Using the null hypothesis that each of the estimated coefficients is not significantly different from zero, and a 5% probably level (or a 5% probability of obtaining the test statistic as large or larger as the one obtained if the true value is in fact zero), the coefficients for GDP and Population are significant (reject the null hypothesis that the true values are 0), while coefficients for the intercept and price are not significant (do not reject the null hypothesis that the true values of the coefficients are zero).

Price:
(a) H0: ?p = 0; HA; ?p ? 0Do not reject at the 5% level (P-value > 0.05)

GDP:
(b)H0: ?gdp = 0; HA; ?gdp ? 0Reject at the 5% level (P-value < 0.05)

POP:
(c) H0: ?pop = 0; HA; ?pop ? 0Reject at the 5% level (P-value < 0.05)

k23.Perform an f-test.

H0: ?p = ?gdp = ?pop = 0;
HA: at least one ? is not equal to zero

Use the analysis of variance (ANOVA) information given in the table below.

ANOVA
dfSSMSFSignificance F
Regression3368163.7122721.259.551154.83988E-16
Residual4796856.22060.77
Total50465019.9
Table 2: F-Test Analysis

F = 59.5515

Critical value
Critical F-Value Calculator:
http://www.danielsoper.com/statcalc3/calc.aspx?id=4

F(3,47) = 2.80235519

Since the 59.5515 > 2.80, reject the null hypothesis. At least one of the ?s is not equal to zero. You can also use the Significance of F information, which indicates that the critical value would need to be essentially zero to not reject the null hypothesis.
Step 1
Download the Regression Analysis Practice document (Excel file).

Step 2
Make sure you have the Data Analysis ToolPak add-in for your Excel. You can do that by going to the Data tab and searching for Data Analysis. If it does not appear, you will need to download it. The steps to download add-ins varies with each version of Excel. Here are the steps for the 2007 version:

Click on the Excel icon in the upper-left corner of your spreadsheet.
Click on Excel Options.
Along the left-side menu, click on Add-Ins.
Select Analysis ToolPak and follow the instructions.

*For Mac users, StatPlus is the recommended free program

Step 3
At the bottom, click on the Demand for Jet Fuel tab. The sample demand equation is estimated using this data set, and the results are shown. For your submission you will be using the Gasoline data on the adjacent tab.

Step 4
Use the procedure described to estimate the demand for gasoline using the same steps identified in the example below. Sample answers are based on the Demand for Jet Fuel data.

1.Evaluate adjusted R2.
The adjusted R2 is 0.778421. It indicates that approximately 78% of the variation in the demand for jet fuel across states is explained by the three independent variablesprice, state GDP, and state population.

2.Evaluate each of the independent variables using a t-test.
Table 1 provides the results of the t-tests for each of the independent variables.

CoefficientsStandard ErrorT-StatP-Value
Intercept-18.449845.28617-0.407410.68556
Price0.1384292.7885820.0496410.960619
GDP0.1700790.0391654.3426467.45E-05
Population0.0052810.0017912.9480360.004967
Table 1: T-Test Analysis

To assist use the Student t-Value Calculator: http://www.danielsoper.com/statcalc3/calc.aspx?id=10
The degrees of freedom are 47, and the probability is 0.05. The critical value is approximately 2. If the absolute value of the t-statistic is greater than 2, the null hypothesis can be rejected. The P-value results can be used to determine whether to reject each of the following hypotheses.

*Using the null hypothesis that each of the estimated coefficients is not significantly different from zero, and a 5% probably level (or a 5% probability of obtaining the test statistic as large or larger as the one obtained if the true value is in fact zero), the coefficients for GDP and Population are significant (reject the null hypothesis that the true values are 0), while coefficients for the intercept and price are not significant (do not reject the null hypothesis that the true values of the coefficients are zero).

Price:
(a) H0: ?p = 0; HA; ?p ? 0Do not reject at the 5% level (P-value > 0.05)

GDP:
(b)H0: ?gdp = 0; HA; ?gdp ? 0Reject at the 5% level (P-value < 0.05)

POP:
(c) H0: ?pop = 0; HA; ?pop ? 0Reject at the 5% level (P-value < 0.05)

3.Perform an f-test.

H0: ?p = ?gdp = ?pop = 0;
HA: at least one ? is not equal to zero

Use the analysis of variance (ANOVA) information given in the table below.

ANOVA
dfSSMSFSignificance F
Regression3368163.7122721.259.551154.83988E-16
Residual4796856.22060.77
Total50465019.9
Table 2: F-Test Analysis

F = 59.5515

Critical value
Critical F-Value Calculator:
http://www.danielsoper.com/statcalc3/calc.aspx?id=4

F(3,47) = 2.80235519

Since the 59.5515 > 2.80, reject the null hypothesis. At least one of the ?s is not equal to zero. You can also use the Significance of F information, which indicates that the critical value would need to be essentially zero to not reject the null hypothesis.

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