in what way is regression analysis useful how well can we evaluate a regression equation fits the data by examining the r square statistic and test for statistical significance of the whole regression equation using the f test quot

discussion about these questions:

“

1. In what way is regression analysis useful?
2. How well can we evaluate a regression equation “fits” the data by examining the R Square statistic, and test for statistical significance of the whole regression equation using the F-Test? “

and I need reply for these ” I agree or I disagree” :

“

1. Regression Analysis is one of the most important quantities technique used in economics. It is statistical tool that can explains the relationship between two variables, one dependent on the other. It explains and predict the direction and degree of correlation between the two variables. Therefore, using this tool help explain the change in dependent variable due to change in other independent variables.

Regression Analysis help explain the data for a business for them to make better decision. It is crucial when it comes to a business’s success. For example, it can help a business to decide how much inventory they should have that maximizes their profit. It can also help them predict the future sales, and other factors that can affect sales.

1. To evaluate overall acceptability of regression equation, we can perform two statistics, one is coefficient of determination, which is “R2”, and the other is the F-statistic, which is used to test whether the overall equation is statistically significant.

R-squared indicates the percentage of the variance in the dependent variable that the independent variables explain collectively. It measures the strength of the relationship between the model and the dependent variable on a convenient 0 – 100% scale.

R-squared is the percentage of the dependent variable variation that a linear model explains. Higher R-squared values represent smaller differences between the observed data and the fitted values and better the regression model fits the data.

An F statistic is used as a test of the overall significance of the included independent variables in a regression model. It measures the ratio of explained to unexplained variation. To measure the significate, we compare f-statist value with critical F-value obtained from an F-table. If the value for the calculated F-statistic is more than the critical F-value, then regression equation is statistically significant.

Generally, If the overall F-test is significant, we can conclude that R-squared does not equal zero, and the correlation between the model and dependent variable is statistically significant.”

“Regression analysis allows us to look at the big picture when it comes to large or small datasets. We can identify whether there is a correlation between our output (y) and all inputs (x). This allows organizations to make data driven decisions with knowledge on which inputs affect the output the most and which ones can be ignored.

R Square is the coefficient of determination. It shows to what extent the variance of one variable explains the other. The higher R squared is, the more that can be explained.

The F test evaluates the ratios of two variables. It helps us answer the question of whether the variance between the means of two populations is significantly different. If f stat is greater than or equal to f critical, the model is considered acceptable.

https://statisticsbyjim.com/regression/interpret-r-squared-regression/“

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