![]() ![]() There are six rows of results (Intercept), age, sex, education, languageFrench, and langaugeOther. The second section, coefficients:, shows us the results from our regression analysis for each independent variable included. We can use these to gage how well or not well are independent varia bles are predicting the dependent varia ble. RStudio provides us with the Min (minimum), 1Q (first quartile), Median, 3Q (third quartile), and the Max (maximum) value of the residuals. Residuals are the predicted values of the independent variables onto the dependent variable. The first section shows us descriptive statistics of the residuals of the model. ![]() We want to minimize this distance between our points and the regression line to have the best fit of our observed points. Lastly, $\epsilon$, is the error term of the regression formula, which is distance of each point ($i$ ) to the predicted regression line. The same goes for $sex(x_2)$, $education(x_3)$, and $language(x_4)$ which are the remaining independent variables, sex, education, and language, that are multiplied by the calculated coefficients in the model. Next, $age(x_1)$, is the variable age multiplied by the calculated regression coefficient that is added to $\beta_0$. We can think of $\beta_0$ as our starting wage value of the observations in the dataset. This is equal to $\beta_0$, the intercept of the model where our regression line intersects with the y axis when $x$ is zero. $_i$, is our dependent variable of the model that we are predicting with four independent variables of a specific observation $i$. $Y_i=\ \beta_0+\ \beta_1x_1+\beta_2x_2\ldots+\beta_kx_k+\varepsilon$įormula 2 is specific to our analysis that includes our dependent variable wages and our independent variables age, sex, education, and language.Ģ.There are two formulas below a general linear regression formula and the specific formula for our example.įormula 1 below, is a general linear regression formula that does not specify our variables and is a good starting place for building a linear regression model. Language is coded as 1= English, 2= French, and 3= Other. This is a nominal level variable measuring the language that each respondent speaks. This is a continuous level variable measuring the number of years of education each respondent has. Education of respondent in years ( education).This is a nominal level variable measuring the sex of each respondent and is coded as 1= FEMALE and 2=MALE. This is a continuous level variable measuring the age of each respondent. This is a continuous variable that ranges from a score of 2.30 to 49.92, which is a large range! If you would like to investigate this variable more use the code for the descriptive statistics to better understand the distribution, which is very important for a linear regression model. Below is a breakdown of the variables included in our model to help us keep track of the types of variables we are working with. ![]()
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