Multiple Linear Regression - Assignment Example

Multiple Linear Regressions al Affiliation: Multiple Linear Regressions Types of F test The two types of F test are Type and Type 3. Type I is called the sequential sum of squares. It is used for testing the main effect of the first factor followed by the second factor and then the interaction effect. Type 3 test identifies the presence of main effects followed by the interaction of these effects.2. R2 and adjusted R2 R2 measures the proportion of the variation on the dependent variable which is explained by the independent variable in a linear regression model.

It also measures how best the regression model fits. Adjusted R2 adjusts the statistics based on the number of independent variables that are in the model. It penalizes the model for including too many parameters that do not contribute much in explaining the original variance. It is a modification of R2.R2 Adjusted R2 3. Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated resulting to inter-associations among independent variables.

This means that one can be linearly predicted from the rest that have non-tribal degree of accuracy. Multicollinearity is a problem because it makes the data unreliable. Multicollinearity is measured using the variance inflation factor that assesses how much the variance of an estimated regression coefficient increases if the predictors are correlated, if not then the variance inflation factor becomes 1.4. Assignment 4 Answer Sheet1. a. b. There is no multicollinearity in the output (a) above since there is no a strong relationship between any two predictor variables.c. I.

North and South variables are significant at 95% level of significance since their p-values are lower than 0.05; p F = 0.0000. This means that the model is significant for estimation of heat flux.d. e. From the residual vs. fitted graph, the residuals appear randomly around zero line. This indicates that the assumption of linearity is reasonable. The normal q-q plot shows that the points re lined up on the identity line and thus, the dependent and independent variables are comparable. Scale-location plot shows that there is a downward trend in residuals.

Cook’s distance’s graph shows that observation 4, 15 and 25 are influential in the model.f. There are outliers in the variables Flux, East and South. Outliers in Flux are observation 19 and 25 which are ==40.6. Thus, we drop observations with outliers in East and South variables. Additionally, observation 4, 15 and 25 are considered to be influential in the dataset.2. a. b. There is no multicollinearity in the above plot. No independent variables are strongly related.c. I. North and South variables are significant at 95% level of significance since their p-values are lower than 0.

05; p F = 0.0000. This implies that the model is significant in estimation of heat flux.d. e. The residual vs. fitted graph shows that residuals appear randomly around the zero line. This indicates that the assumption of linearity is reasonable. The normal q-q plot shows that the points re lined up on the identity line and thus, the dependent and independent variables are comparable. Scale-location plot shows that there is a downward trend in residuals. Cook’s distance’s graph shows that observation 3, 13 and 22 are influential in the model.f. The predicted fit is 248.

1639 which lie between 210.6848 and 285.643 as the predicted intervals. Additionally, the predicted fit has a confidence interval (218.288, 278.0398) for lower and upper bound respectively. 3. a. Insolation and East variables are droppedb. Eliminating the variables improves the model. In the previous model, with four predictor variables, we obtain a coefficient of determination = 0.812 whereas in the reduced model, with two predictor variables, = 0.806. Thus, the dropped variables account for only 0.

06 which is quite insignificant for the model.c. d. The residual vs. fitted graph depict that residuals appear randomly around the zero line. This implies that the assumption of linearity is reasonable. The normal q-q plot shows that the points are lined up on the identity line and thus, the dependent and independent variables are comparable. Scale-location plot shows that there is a downward trend in residuals. Cook’s distance’s graph shows that observation 3, 13 and 22 are influential in the model.e. i. = 4ii. =2iii. =11229.4078 iv. = 11162.6474v.

F-statistic = 0.01189028vi. P-value = 0.9883036vii. Since p-value is larger, we fail to reject the null hypothesis and conclude that the reduced model is better than the full model ReferenceWang, George & Jain, Chaman. Regression Analysis: Modeling & Forecasting. Institute of Business Forec. 2003. Print