Created on 2024-06-20Asked by Elijah Clark (Solvelet student)
Perform a linear regression analysis on the following data set: {(1,2),(2,3),(3,5),(4,4),(5,6)}.
Solution
To perform a linear regression analysis on the data set {(1,2),(2,3),(3,5),(4,4),(5,6)}: 1. **Calculate the means of x and y:** xˉ=51+2+3+4+5=3,yˉ=52+3+5+4+6=4. 2. **Calculate the slope m:** m=∑i=15(xi−xˉ)2∑i=15(xi−xˉ)(yi−yˉ),m=(1−3)2+(2−3)2+(3−3)2+(4−3)2+(5−3)2(1−3)(2−4)+(2−3)(3−4)+(3−3)(5−4)+(4−3)(4−4)+(5−3)(6−4),m=4+1+0+1+4(−2)(−2)+(−1)(−1)+(0)(1)+(1)(0)+(2)(2),m=104+1+0+0+4=109=0.9. 3. **Calculate the y-intercept b:** b=yˉ−mxˉ=4−0.9⋅3=4−2.7=1.3. 4. **Form the regression equation:** y=0.9x+1.3. Therefore, the linear regression equation for the data set is y=0.9x+1.3. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Benjamin Scott on Solvelet
DefinitionRegression analysis is the statistical method by which relationships between variables are modeled. It embodies the methods to evaluate the model and set the relationship between a dependent variable and one or more independent variables. For instance: if there is a set of points and an outcome of a linear regression that can be used to predict the outcome, the linear regression will best fit the straight line.
