7 Regression for Business Analysis Free Online FlashCards

What does regression estimate?

Regression estimates how an outcome varies with one or more factors and can support explanation or prediction.

Does regression alone prove that a predictor causes an outcome?

No. Regression estimates associations; omitted factors or other issues can affect both variables. Causal claims usually require a suitable experimental or causal-inference design.

What is a regression residual?

A residual is the observed outcome minus its predicted value: $y_i-\hat y_i$.

What does ordinary least squares minimize?

Ordinary least squares estimates coefficients by minimizing the sum of squared residuals.

How should a coefficient in multiple regression be interpreted?

Each coefficient describes the predictor’s association with the outcome while the other included predictors are held constant.

In the sales example, what does the advertising coefficient $2.4$ mean?

Holding price constant, an additional $\$1{,}000$ in advertising is associated with an estimated $\$2{,}400$ increase in weekly sales.

How does a prediction interval differ from a confidence interval?

A confidence interval gives a range of plausible values for a coefficient. A prediction interval describes uncertainty for an individual future outcome and is usually wider.

What does a small p-value establish about a regression effect?

A small p-value is evidence against a zero coefficient under the model, but it does not show that the effect is large, useful, or causal.

What does the linearity assumption require?

The expected outcome should follow the specified relationship. Curves or systematic patterns in residual plots can indicate that the model is missing structure.

What does the independent-errors assumption rule out?

Residuals should not show dependence, such as patterns across successive days or repeated observations from the same customer.

What does a fan-shaped residual pattern suggest?

Residual spread should be roughly similar across fitted values. A fan-shaped pattern suggests changing variance, which can make standard errors and intervals unreliable if ignored.

What is a consequence of severe multicollinearity?

Predictors that move closely together can make their individual coefficients unstable and hard to interpret, even when overall predictions are adequate.