Regression Analysis

Regression is a statistical technique applied in investing, finance, and other disciplines that tries to determine the strength and character of the association between one dependent variable and a list of other independent variables. Regression analysis is designed to use observations to quantify the association between an objective variable and a set of independent variables. In simple regression, there is just one independent variable and one dependent variable, which can be adequately approximated by a linear function.

Concerning the importance of regression in a business, it helps in making informed strategic plans. For instance, managers can weigh the components of a business that are most important to prioritize them. They also identify how various business factors are related to one another.  The technique is of value since comparing variables of concern in decision making is a statistical way of testing expected outcomes. Regression analysis also helps an organization understand its data and effectively use the data points in strategic decision-making through business analytical methods. The regression technique of forecasting means examining the relationships between data points, which can help managers to foretell sales in the near and long course, know inventory levels, and learn supply and demand.

I chose the dataset of Test Scores. The dependent variable will be Exam Grades, and the independent variable is Minutes of Study Time. It will be necessary to know if the amount of time a student spends studying has an impact on their exam results. As such, I need to predict if Exam Results depend on the time spent studying. I will assume that the more time spent studying, the higher the exam grades.

Table1: Regression Statistics

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.921702393
R Square	0.849535302
Adjusted R Square	0.842993358
Standard Error	5.170041975
Observations	25

R Squared, which is 0.8495, means that 84.95% of Y’s variation is being explained by X.
Twenty-five observations mean that we had 25 variables.

Table 2: Anova

ANOVA
	df	SS	MS	F	Significance F
Regression	1	3471.065318	3471.065318	129.8597756	6.15511E-11
Residual	23	614.7746824	26.72933402
Total	24	4085.84
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	48.0762754	2.992730824	16.06435	5.39488E-14	41.88534001	54.2672108
Minutes Study Time, X	0.212508131	0.018648256	11.39560335	6.15511E-11	0.173931274	0.251084989