![]() the value of y where the line intersects with the y-axisįor our purposes, we write the equation of the best fit line asįor each i, we define ŷ i as the y-value of x i on this line, and so Recall that the equation for a straight line is y = bx + a, whereĪ = y-intercept, i.e. We now look at the line in the xy plane that best fits the data ( x 1, y 1), …, ( x n, y n). For example, a student who studies for three hours and takes one prep exam is expected to receive a score of 83.75:Įxam score = 67.67 + 5.56*(3) – 0.60*(1) = 83.In Correlation we study the linear correlation between two random variables x and y. We can use this estimated regression equation to calculate the expected exam score for a student, based on the number of hours they study and the number of prep exams they take. In this example, the observed values fall an average of 5.3657 units from the regression line.Įstimated regression equation: We can use the coefficients from the output of the model to create the following estimated regression equation:Įxam score = 67.67 + 5.56*(hours) – 0.60*(prep exams) This is the average distance that the observed values fall from the regression line. In this example, 73.4% of the variation in the exam scores can be explained by the number of hours studied and the number of prep exams taken. It is the proportion of the variance in the response variable that can be explained by the explanatory variables. This is known as the coefficient of determination. The following screenshot shows how to perform multiple linear regression using a dataset of 20 students with the following formula used in cell E2: To explore this relationship, we can perform multiple linear regression using hours studied and prep exams taken as explanatory variables and exam score as a response variable. Suppose we want to know if the number of hours spent studying and the number of prep exams taken affects the score that a student receives on a certain college entrance exam. For example, a student who studies for three hours is expected to receive an exam score of 82.91:Įxam score = 67.16 + 5.2503*(3) = 82.91 Multiple Linear Regression in Google Sheets We can use this estimated regression equation to calculate the expected exam score for a student, based on the number of hours they study. We interpret the coefficient for the intercept to mean that the expected exam score for a student who studies zero hours is 67.16. We interpret the coefficient for hours to mean that for each additional hour studied, the exam score is expected to increase by 5.2503, on average. In this example the estimated regression equation is: In this example, the observed values fall an average of 5.2805 units from the regression line.Ĭoefficients: The coefficients give us the numbers necessary to write the estimated regression equation. In this example, roughly 72.73% of the variation in the exam scores can be explained by the number of hours studied. It is the proportion of the variance in the response variable that can be explained by the explanatory variable. Here is how to interpret the most relevant numbers in the output: The following screenshot provide annotations for the output: ![]() The following screenshot shows how to perform simple linear regression using a dataset of 20 students with the following formula used in cell D2: To explore this relationship, we can perform simple linear regression using hours studied as an explanatory variable and exam score as a response variable. studies for an exam and the exam score they receive. Suppose we are interested in understanding the relationship between hours studied and exam score. Simple Linear Regression in Google Sheets The following examples show how to use this function in practice. This is FALSE by default, but we will specify this to be TRUE in our examples.
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