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# BNAD277 Chapter 14a Notes BNAD277

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This 6 page Class Notes was uploaded by Kristin Koelewyn on Tuesday April 19, 2016. The Class Notes belongs to BNAD277 at University of Arizona taught by Dr. S. Umashankar in Spring 2016. Since its upload, it has received 12 views. For similar materials see Business Statistics in Business at University of Arizona.

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Date Created: 04/19/16

Bnad277: Chapter 14a Notes Simple Linear Regression - Managerial decisions often are based on the relationship between two or more variables. - Regression analysis can be used to develop an equation showing how the variables are related. - The variable being predicted is called the dependent variable and is denoted by y. - The variables being used to predict the value of the dependent variable are called the independent variables and are denoted by x. - Simple linear regression involves one independent variable and one dependent variable. - The relationship between the two variables is approximated by a straight line. - Regression analysis involving two or more independent variables is called multiple regression. - Simple Linear Regression Model: o The equation that describes how y is related to x and an error term is called the regression model. o The simple linear regression model is: ▯ where b a0d b are1called parameters of the model, e is a random variable called the error term. o The simple linear regression equation is: o Positive Linear Relationship: o Negative Linear Relationship: o No Relationship: - Estimated Simple Linear Regression Equation: - Estimation Process: o - Least Squares Method: o Least Squares Criterion o Slope for the Estimated Regression Equation o y-Intercept for the Estimated Regression Equation: - Simple Linear Regression: o Example: Reed Auto periodically has a special week-long sale. As part of the advertising campaign Reed runs one or more television commercials during the weekend preceding the sale. Data from a sample of 5 previous sales are shown on the next slide. - Estimated Regression Equation: o Slope for the Estimated Regression Equation o y-Intercept for the Estimated Regression Equation o Estimated Regression Equation - Coefficient of Determination: o Relationship Among SST, SSR, SSE o The coefficient of determination is: - Sample Correlation Coefficient: - Assumptions About the Error Term e - Testing for Significance: 2 o An Estimate of s ▯ The mean square error (MSE) provides the estimate of s , 2 and the notation s is also used. o An Estimate of s - Testing for Significance: t Test o Hypothesis: o Test Statistic: o Rejection: o Step 1: Determine the Hypothesis o Step 2: Specify the level of significance o Step 3: Select the test Statistic: o Step 4: State the Rejection Rule o Step 5: Compute the value of the test statistic o Step 6: Determine whether to reject Ho - Confidence Interval b 1 o We can use a 95% confidence interval for b to test1the hypotheses just used in the t test. o H i0 rejected if the hypothesized value of b is no1 included in the confidence interval for b . 1 o The form of a confidence interval for b is: 1 ▯ where t a/2 is the t value providing an area of a/2 in the upper tail of a t distribution with n - 2 degrees of freedom o Rejection Rule: Reject H if 00is not included in the confidence interval for b 1 o 95% Confidence Interval for b 1 o Conclusion: 0 is not included in the confidence interval. Reject H 0 - Testing for Significance: F Test o Hypothesis: ▯ o Test Statistic: o Rejection Rule: - Some Cautions about the Interpretation of Significance Tests: o Rejecting H : b =00 a1d concluding that the relationship between x and y is significant does not enable us to conclude that a cause- and-effect relationship is present between x and y. o Just because we are able to reject H : b = 0 an0 de1onstrate statistical significance does not enable us to conclude that there is a linear relationship between x and y.

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