statistics: 6.1 SIMPLE LINEAR REGRESSION

what is linear regression? 2 pts

its a data analysis technique that predicts the value of unknown data by using another related and known data value; a statistical model of the unknown dependent variable and the known independent variable as a linear equation that allows us to predict the relationship between two or more variables

what is a statistical model? 1 pt

a formal representation of reality expressed using mathematical terms and equations

what is the goal of linear regression? 2 pts

1. to study the effect of the IV/predictor over the DV/putcome

2. to predict possible values of the DV/outcome

linear regression vs correlation? 3 pts

1. when we use correlation we are looking at the relationship between two variables

2. when we use regression we are trying to predict one variable using the other one

3. the distinction beyween IV/predictor and DV/outcome is key

variables of a linear regression? 3 pts

1. a DV that is a scale variable (interval/ratio)

2. an IV that can be a scale, nominal, or ordinal variable

3. predictors/IV can be any type while outcomes/DV have to be scale variables

what is a regression line? 1 pt

the straight line that goes through the middle of the data in a scatterplot

regression line: important notes?

1. we should only talk about how the outcome (DV) changes when the predictor (IV) changes according to the regression line that we fit to the data

2. we cannot say for sure that outcome changes because the predictor changes as there could be confounders that are unaccounted for

3. linear regression line represents an equation/model that is never perfect

4. the best regression line is the one that minimizes the amount of error in the prediction by using the values of the slope and intercept that minimize total amount of error

slope vs intercept? 2 pts

1. intercept- the location where the line intersects the y-axis

2. slope- the steepness of the line

regression line formula? 5 pts

y = a + b + x X + error

1. y→ dependent variable/outcome

2. x→ independent vairable/predictor

3. a→ intercept (predicted when the value of X is 0)

4. b→ slope or regression coefficient

the slope? 3 pts

1. the slope/regression coefficient represent the inclincation of the line

2. it represents the amount of change in the outcome due to a change of 1 unit in the predictor

3. if it is a positive number the relationship is positive, if it is a negative number the relationship is negative

the intercept? 2 pts

1. the intercept represents the point where the line cuts the vertical axis

2. it is the value predicted for someone who scores a zero in the independent variable

how do we calculate the regression line? 3 pts

1. we need to calculate the slope/regression coefficient and the intercept

2. once we have tthese values we can add the predictor (x) and outcome (y) to the formula

3. we can obtain the outcome

assumption checks for simple linear regression? 6 pts

1. the DV is measured at the continous level (interval or ratio)

2. the IV is measured at the continous level (interval or ratio) but can also be nominal or ordinal

3. there is a linear relationship between x and y that can be evaluated using a scatterplot

4. there should be no significant outliers as they can reduce the predictive accuracy of the results

5. homoscedasticity- where the variances alone the line of best fit remain similar as you move along

6. residual errors of the regression line are approximately normally distributed which can be confirmed by looking at the distribution of residuals