I performed a multiple regression analysis and three scores of the independent variables have a negative sign. How do I interpret this inverse influence on the dependent variable?
You have y=b0+b1x1 + b2x2 +e
It turns out that b2 is -4.3. This means that as x2 increases by 1 unit, y decreases by 4.3 units. It becomes more difficult if x1 and x2 are correlated, but that violates the independence assumption of the model.
Dear Timothy Ebert, Thank you so much for your useful answer. I am measuring the cabinet partisan homegeinity/hetrogeinity in cabinet turnover and found that the cabinet partisan index I constructed, had a negative coefficient. According to your answer the inrease in the partisan Index means a decrease in the cabinet turnover index. Thank you again.
Yes, Timothy explains the interpretation of the negative coefficients. Plug that into your model, the real-life interpretation may be counter-intuitive though that depends on what you code homegeinity/hetrogeinity, turnover and their relationship with cabinet partisan.
Furthermore, the negative coefficients are correcting the prediction of the positive coefficients. What are the positive ones? Could there be interactions that should be included in the model?
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