Questions the Linear Regression Answers
There are 3 major areas of questions that the regression analysis answers –
(1) causal analysis,
(2) forecasting an effect, and
(3) trend forecasting.
The first category establishes a causal relationship between two variables, with the dependent variable being continuous and the predictors being categorical (dummy coded), dichotomous, or continuous. In contrast to correlation analysis which does not indicate directionality of effects, the regression analysis assumes that the independent variable has an effect on the dependent variable.
Examples:
Medicine: Has the body weight an influence on the blood cholesterol level? To answer this question the researcher would measure body weight and blood cholesterol level in various subjects. The linear regression analysis can then show whether the body weight (independent variable) has an effect on the blood cholesterol level (dependent variable).
Biology: Does the oxygen level in water stimulate plant growth? The research team would measure different concentrations of oxygen in the water and measure the growth of plants. Linear regression analysis can then establish whether a causal relationship exists between the independent and dependent variables. It is particularly useful for testing observations made in experimental conditions, such as when researchers deliberately manipulate the oxygen level in the water to test its effects.
Management: Does customer satisfaction influence loyalty? The research team would ask customers to rate their satisfaction and also their loyalty to the company. The analysis can then prove the assumed causal relationship of satisfaction on loyalty.
Psychology: Is anxiety influenced by personality traits? To answer this question the team of researchers would measure anxiety (e.g. BAI) and one personality trait (e.g., consciousness). Linear regression analysis tests whether a causal link exists between both variables. However, it does not prove that the causal direction is from anxiety to personality or the other way around.
Secondly, it can be used to forecast values:
Medicine: With X cigarettes smoked per day, life expectancy is Y years. The research team observes smoking habits and age at death in a group of participants. The regression coefficient in y = a + b*x shows life expectancy changes per cigarette smoked. cigarette smoked per day.
Biology: Five additional weeks of sunshine the sugar concentration in vine grapes will rise by X %. In a sample measuring sunshine duration and grape sugar levels, linear regression establishes the formula y = a + b*x. It is especially useful when the x variables are not entirely random.
Management: With X dollars spent on marketing, sales should be Y. The researcher uses linear regression (y = a + b*x) to predict sales (y) from marketing spend (x).
Thirdly, to predict trends in data one can use linear regression analysis:
Medicine: How much does life expectancy decrease per pound overweight? Linear regression predicts trends, even if the intercept isn’t significant, using the regression coefficient (if significant).
Biology: Each week of sunshine increases grape sugar by Y%. The regression coefficient shows the trend, with the dependent variable rising by b*x. This helps when x values aren’t random, violating ANOVA and correlation assumptions.