# Multiple regression question

$H_0: B_0=B_1=B_2=B_3 ... =0$
$H_1: \text{ at least one is not equal to zero}$

I am doing a research project and I am lost trying to figure out this problem. I have negative coefficient, I have dependent variable and 5 independent variables, due to the dependent variable data being from different years and on other ind. var as well I had to standardize the data.

My $R^2$ is very low and the adjusted $R^2$ as well.

The coefficients are negative, I do not know how to interpret this information.

When I standardized all the data dep. and ind. variables this made the majority negative, and because of negative I have negative Betas, and I don't now know what to do with negative betas.

sorry this is my first time doing such a project.

I have attached a print screen of the problem

• Dear whuber, thank you for the prompt respond, I have updated the questions. It is my first time and I am having to interpret the results. especially having negative (betas) and I should reject the H0 because my p value is <.05 right? – Säb Jun 14 '17 at 9:18
• what prompted you to standardize the data? please give a few details of data and objective of research. – Subhash C. Davar Jun 14 '17 at 13:15
• Are you interested in hypothesis testing or merely sign of regression coefficients ? – Subhash C. Davar Jun 14 '17 at 16:37

## 1 Answer

There is nothing special about the coefficients being negative, it just means that the relationship is inverse. That is, as the independent variables go up, the prediction of the dependent variable goes down.

As to R^2 being "low", well, you don't say what field you are working in, but in many fields, an R^2 of 0.40 would be quite acceptable.

Of course, you still need to check all the assumptions of multiple regression.

• thank you for your feeback Mr. Flom, this is finance project and depended variable is the cost of capital and indep. are the earnings, leverage, sell-side analysis and free float. I have check assumptions of multiple regression using t-test and f-test, are these reliable to reject H0 or do I need to do further assumptions? thank you again – Säb Jun 16 '17 at 9:34
• You cannot check the assumptions using t-tests and f-tests. Are the residuals normal? Is there heteroskedasticity? Is there collinearity? Are there outliers? Is the data independent? In particular, if this is time series data, you are going to have issues. – Peter Flom - Reinstate Monica Jun 16 '17 at 13:24
• Thank you for quick feedback Mr. Flom, I think the data is depended, and the residuals are in a shape of an egg, and i did Q Q Plot of dependent variable and it is in a shape of S, especially the negative is begins in a straight line then starts to rise. I am checking on the heteroskedasticity (with an residual R2 as y and inde. variables as x , the p-value is 002) collinearity i will check later today. Many thanks to you Sir. – Säb Jun 16 '17 at 16:46
• ICC 100% EARN VOLA 0.61% 100% LEVERAGE -4.39% -10.44% 100% FREE FLO -34.54% -24.46% 17.37% 100.00% SELL-SIDE 41.61% 2.91% 2.83% 23.31% 100.00% SURPRISE 0.42% 34.90% 7.86% -1.59% 1.17% As you can see from data above some are correlation and some are not – Säb Jun 16 '17 at 16:54