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Statistical Methods for Research 1. Discuss and describe the basics of regression; What are we trying to accomplish; How does regression work 2. Discuss the underlying assumptions of a simple linear regression model: multiple regression model: and polynomial regression model. 3. Consider the below regression output. Note that some values have been erased. In order to solve all parts of this problem, you may have to find all the missing values first. SUMMARY OUTPUT Regression Statistics Multiple R 0.9613 R Square Adjusted R Square 0.9222 Standard Error Observations 200 ANOVA Significance df SS MS F F Regression 479410417802.47 95882083560.49 0.00 Residual 202929702.05 Total 518778780000.00 Upper Coefficients Standard Error Stat P-value Lower 95% 95% Intercept 45482.366 19403.8863 2.34 0.0201 v1 -10383.543 3153.7202 -3.29 0.0012 v2 11.088 10.4859 1.06 0.2916 v3 738.388 175.8223 4.20 0.0000 v4 0.014 0.0023 6.37 0.0000 v5 -2.546 1.2209 -2.09 0.0383 a. Give the regression model from the table. b. Determine the degrees of freedom (and fill in the blanks in the table). c. Find the Error Sum of Square (SSE) (and fill in the blank in the table). d. For testing the significance of overall regression find F-calc (and fill in the blank in the table). Conduct the hypothesis test; Is regression significant. e. Find the standard error for the data (and fill in the blank in the table). 1 Statistical Methods for Research f. Find the coefficient of determination, R-squared, (and fill in the blank in the table). Give an interpretation of the value of R-squared. g. Find the 95% confidence intervals for all parameters; (and fill in the blanks in the table). Assume that the critical t-value for a 95% confidence interval is 1.96 (from a t-table) h. Conduct all parameter tests using alpha = 0.05 (5%). Which parameters are significant; wh Which parameters are borderline significant/not-significant; why Which parameter is the most significant; least significant; why 2

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1. Regression is used to find the relationship between independent variables and a dependent variable. Then the relation can be used to make the future predictions of dependent values based on independent variables. The set of independent variables are also termed as predictors and dependent variable as response variable. E.g. if we want to find the relationship between the cost of house on the basis of its area, number of bedrooms, num of floor etc, the cost is the response variable while all other parameters are predictors. Regression can be used to find the weight/coefficient given to each predictor
which can be used to estimate the cost of the house. For example the relation can be:
cost = 10000*area + 5000*num_of_beds - 100 * floor_number.   
It shows increase of one unit of area increases the cost by 10000 times. Similarly, each increase of floor number deceases the cost of house by a factor of 100. This is an example of simple linear regression.
Similarly, a combination of predictors can be used as a predictor, this type of regression is called the multiple regression. Regression using predictors with power more than one are called polynomial regression....

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