Question : Which of the following statement true with regards to Linear Regression Model? A. Ordinary Least Square can be used to estimates the parameters in linear model B. In Linear model, it tries to find multiple lines which can approximate the relationship between the outcome and input variables. C. Ordinary Least Square is a sum of the individual distance between each point and the fitted line of regression model. D. Ordinary Least Square is a sum of the squared individual distance between each point and the fitted line of regression model.
1. A,B 2. B,C 3. C,D 4. A,D 5. B,D
Correct Answer : 4 Explanation: Linear regression model are represented using the below equation Y=B(0) + B(1)X Where B(0) is intercept and B(1) is a slope. As B(0) and B(1) changes then fitted line also shifts accordingly on the plot. The purpose of the Ordinary Least Square method is to estimates these parameters B(0) and B(1). And similarly it is a sum of squared distance between the observed point and the fitted line. Ordinary least squares (OLS) regression minimizes the sum of the squared residuals. A model fits the data well if the differences between the observed values and the model's predicted values are small and unbiased.
Question : Which of the following is correct definition of Residual?
1. Residual is a mean squared error
2. Residual is calculated as square of actual value minus predicted value
3. Residual is calculated as Actual Value minus Predicted Values
4. Residual is calculated as Actual Value plus Predicted Values
Correct Answer : 3 Explanation: Residuals are errors in Linear Regression model and can be calculated using the Actual value minus Predicted Value. It can be positive or negative.
Question : Which of the following statement is true with regards to R square? A. It helps in finding that how close the data are to the fitted model. B. R Square has value between 0 to 999 C. R square 0 means the model explains none of the variability of the response data around the mean. D. R square 999 indicates that the model explains all the variability of the response data around mean. E. Higher the squared, the better the model fits your data.
1. A,B 2. B,C 3. A,C 4. D,E 5. A,E
Correct Answer : 3 Explanation: R square is a statistical measure to find that how close the data are in the fitted regression line. This is known as coefficient of determination. R Square is the percentage of the response variable variation that is explained by a linear model Which you can say R square = Explained Variation/Total Variation R square always have value between 0% and 100% Where 0% represents that the model explains none of the variability of the response data around the mean. And 100% represents that model are able to explain all the variability around the mean. Hence, if your model could explain the the 100% of the variance, the fitted values would always equal to the observed values and you can say that all the data points would fall on the fitted regression line.