Using Microsoft Excel to Conduct Regression Analysis

Example MarketsPriceQuantity What do we know? Price and quantity of pens in 15 markets with similar characteristics. -What do we want to know? The relation between price and quantity, i.e., the demand curve. -Proposed Model Specification: Finding the demand curve where quantity (Q) is the dependent variable and price (P) is the explanatory variable. -What we want to know: (a)estimate of parameters (b)parameter testing (c)forecasting

Step 2: Run Regression in Excel 1.Click “Data Analysis” in “Tools” box. 2.Click “Regression” in “Data Analysis” box. 3.Setup in “Regression” window including: a)Input Y range: Quantity (P1:P16). b)Click “Label” is you want to have labels in output. c)Confidence level: 95%. d)Output options:

Step 3: Regression Results

Interpret Regression Output Estimated Linear Demand Function Intercept: Price coefficient: What proportion of variation of Y is explained by the regression? R² = 0.74; Estimates of standard error: Estimates of variance: = 3.02

Tests Based on Regression Results

The t-Test Example: H 0 : b = -0.3 Step 1: Step 2: - Degrees of Freedom = 15 – 2 = 13, 2-tailed test - One method: compare t-stat and c value t-stat: < -c = Another method: finding out p-value p = tdist(3.51, 13, 2) = Step 3: - Reject the null hypothesis - Why? < or p = < 0.05

The t-Test Example: H 0 : b > -0.1 Step 1: Step 2: - DF = 15 – 2 = 13, 1-tailed test, significant level 5% - One method: compare t-stat and c value t-stat: < -c = -t(0.10, 13, 1, 5%) = Another method: compare p-value and significant level p = tdist(2.905, 13, 1) = Step 3: - Reject the null hypothesis - Why? t stat = < -c = or p = < 0.05

Confidence Interval of a = Calculate 95% CI of a = How? - CI of coefficient: - The critical value of c is 2.16, given DF = 15 – 2 = 13, level of confidence = 5%, and two-tailed test. - se(estimate) = 2.09 is the standard error of the estimate. Interpretation: - Any number outside of the CI is statistically different than the estimated a = Any number within the CI is statistically no different than the estimated a = 28.92

Confidence Interval: b = How? - CI of coefficient: - The critical value of c is 2.16, given DF = 15 – 2 = 13, level of confidence = 5%, and two-tail. - se(estimate) = 0.03 is the standard error of the estimate. Results: Interpretation: - Any number outside the CI is statistically different from at the 5% level. - Any number within the CI is statistically no different than the estimated b =