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ANALYSIS
Multiple Linear Regression Analysis Name Course Professor 10/4/2017 Multiple Linear Regression Analysis DS411 Case1 SUMMARY OUTPUT Regression Statistics Multiple R	0.119464442 R Square	0.014271753 Adjusted R Square	0.012323673 Standard Error	8.307214996 Observations	2029

The objective for this multiple linear regression analysis was to determine if there existed any collinearity between significant mutual funds return and the predictor variables. From the multiple linear regression analysis, the predictor variables were SAT units, degree qualification units, age units, and tenure units and therefore, the formula for predicting the predicted mutual funds return was found to be: The R square for the predictor equation was a weak one since it was equal to 0.0143 which meant that the significance of the model was not attained. Conclusively, the simple linear regression model was not a good fit. For the variables used in the regression analysis, only two are adding to the model; SAT units and age units, but degree units and tenure units do not. It is also important to note that on average, the estimates of the predicted mutual funds with this model will be wrong by 8.31 points. Now, since the p-value = 0.00000743054 < .05 = α, we conclude that the regression model is a significantly good fit; i.e. there is only a 0.00% possibility of getting a correlation this high (0.119) assuming that the null hypothesis is true. From this analysis and conclusion, we have a conclusion that the model is not a good fit for predicting the predicted mutual funds. This is basically due to the fact that there are two predictor variables which are significant while the other two are not significant. As seen from the residual output, a plot of the data reveals that there is not linearity and homogeneity. The result we have, prove that in the case of collinearity, the predictor variables have less correlation and for this fact, they do not relate to each other. Looking at all of them, we discovered that only one coefficient is significant and it is that of age. Now, this implies that the predictor variable age is the only one which can be used to significantly predict the predicted mutual funds. This is in the form of making sure only the relevant and significant coefficients are used in the regression analysis and for this reason, we now a linear regression model which will use only one predictor variable. Home Sales with Dummy SUMMARY OUTPUT Regression Statistics Multiple R	0.866965704 R Square	0.751629531 Adjusted R Square	0.73295506 Standard Error	7.240313942 Observations	144

The regression analysis conducted for the data provided was that of a multiple linear regression and the model resulted with 13 variables; where we had MR, ICS, and the months of February to December. Now, the following model resulted from the multiple linear regression analysis: Y = 104 – 11.6538MR + 0.44530577ICS + 9.442397269Feb + 19.6556595Mar + 16.2270962Apr + 15.53226345May + 13.424011Jun + 10.78153101Jul + 13.55585648Aug + 5.889924456Sep + 4.12853Oct – 1.76619Nov – 5.38326Dec From the summary output, the R square for the predictor model was found to be 0.77 a clear indication that the multiple linear regression model was significant for the given data. The 13 predictor variables included were also significant for the model given that from the ANOVA analysis, the significance was found to be 2.17262E-35. Therefore, we have a p-value = 2.17262E-35 < .05 = α and hence our conclusion was that the regression model was significantly a good fit. It had the possibility of 0.00% possibility of getting a correlation this high (0.8784) assuming that the null hypothesis is true. It therefore follows that 10 of the 13 variables are significant for the multiple linear regression model since they have a p-value < 0.05 implying that the model generated from these coefficients will have a relatively significant model. This goes further to indicate that the inclusion of many variables for the multiple linear regression model have an effect on the resulting model. This is because the model has to deal with different factors that are aimed at representing a single linear model from the multiple predictors which can be used to forecast the future. Now, considering the standard error, we know that the predicted value is set to be wrong by 7.02 points using the multiple linear regression model which has been generated from the provided data. Travel Expenses SUMMARY OUTPUT Regression Statistics Multiple R	0.90979634 R Square	0.82772937 Adjusted R Square	0.8080413 Standard Error	100.630923 Observations	40

The multiple linear regression analysis, the predictor variables were days on the road, miles driven, north and south which resulted with the following model: Now, looking at the summary output, the R square for the predictor model was found to be 0.8277, a clear indication that the model was significant for the regression analysis. The analysis included two dummy variables; North and South that acted as an indicator of the direction the traveler went. Now, since the p-value = 0.00000000000067 < 0.05 = α, we conclude that the regression model is a significantly good fit; i.e. there is only a 0.00% possibility of getting a correlation this high (0.909) assuming that the null hypothesis is true.