smoking-multi-regression
Description of Research
-The Analysis to be conducted here is a linear regression model from the dataset. -Here, as we are trying to find the effect of smoking on expenses, the independent variable is “smoker”, and the dependent variable is “expenses”. -Taking into consideration the dataset, the following will our null and alternative hypothesis: -Ho (Null Hypothesis): expenses are not correlated with the variable smoker -Ha (Alternative Hypothesis): expenses is correlated with the variable smoker -We will either reject the Null Hypothesis and accept Alternative Hypothesis, or vice versa. -The next analysis to be conducted here is a multivariate regression model from the dataset. -Here, as we are trying to find all input variables on expenses, the independent variables will be all input variables, and the dependent variable is “expenses”. -To answer the research question, we will use a histogram, t-test, build a linear and multi regression model.
Exploratory Data Analysis
-We created a Histogram for the variable “expenses”. -Here, we can see that the data is positively skewed. -The values from 0 to 15000 are much more than the rest of the dataset for the variable “expenses”. -We will look further into how this skewed data impacts our analysis.
T Test
-The Analysis to be conducted here is a T-test. -Here, as we are trying to find if the mean for expenses is equal to 10000 or not. -Taking into consideration the dataset, the following will our null and alternative hypothesis: -Ho (Null Hypothesis): the mean for expenses is equal to 10000 -Ha (Alternative Hypothesis): the mean for expenses is not equal to 10000 -We will either reject the Null Hypothesis and accept Alternative Hypothesis, or vice versa. -There are a few assumptions that we need to satisfy to conduct the T-test. -These are that the data is normalized, and there is an equality in the standard deviation and the variance. -By looking at the histogram we build earlier, we can see the skewness in the data. -We must be careful when we analyze the findings of T-test as the data is not normalized. -We should still carry out the T-test to know how the skewness influences the output.
Simple Linear Regression
-In the Simple Linear Regression Model that we carried out, we can see that the R square value is 0.6198 -As we know the R squared value shows the statistical significance of the model. -At 0.6198 it seems to be good, but when we see the p-value which is quite low, we can get to know that one should not trust R squared totally. -As the p-value at 2.02e-16 is much lower than 0.5 which is the statistical significance level, we can say that the model does now depict good accuracy.
Multivariate Linear Regression
-In the Multi Regression Model that we carried out; we can see that the R square value is 0.7509 -As we know the R squared value shows the statistical significance of the model. -At 0.7509 it seems to be good, but when we see the p-value which is quite low, we can get to know that one should not trust R squared totally. -Also, as we see that the residual standard error is 6062 on 1329 degrees of freedom which shows the quality of the fit of the model. -This also shows how close our estimates are. -As the p-value at 2.02e-16 is much lower than 0.5 which is the statistical significance level, we can say that the model does now depict good accuracy.
Conclusion
-The conclusion we could make out from the histogram is that the data was heavily skewed positively and that affected to a great extent when it came to impact on the model. -Evidence like the T-test is also biased, and we cannot trust it fully when it comes to predictions for modeling. -We recommend to normalize the data and make the data more balanced. -This will make the exploratory analysis as well as our T-tests and other basic statistics more relevant to the model that we could build on it. -Also, the model will be more accurate, and there could be real insights that we could find from the whole analysis.