tailieunhanh - Data Analysis and Presentation Skills Part 7

Tham khảo tài liệu 'data analysis and presentation skills part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 102 4 PRELIMINARY DATA ANALYSIS from a hand-drawn plot where the line of best fit has been drawn in by placing a ruler onto the plot and determining the best place to draw the line manually we now have a more accurate means of quantitating our unknown value. This means rearranging Equation to solve for x x y Equation So if we had an absorbance reading of then if we substitute this in the rearranged equation we should obtain a value of mg ml for concentration. Multiple regression In the previous sections we have investigated the relationship between one independent variable and another dependent variable . There may be times however when we suspect that there is a relationship between more than two variables and that these are interdependent. To determine how to relate these variables we must use multiple regression. In simple linear regression we demonstrated the relationship between x and y as y mx c Equation In multiple regression we imply that y is linearly dependent on one variable x1 and also dependent on another variable x2 so y m1x1 m2x2 c Equation This equation assumes that the dependent variable y is dependent on two independent variables x1 and x2. m1 and m2 are partial regression coefficients because they can reflect how a value of y would change with a unit change of x1 if x2 were held constant and vice y is dependent on more than one variable then the equation may be adapted to include as many variables as necessary. So if y is dependent on four variables then y mix1 m2x2 m3x3 m4x4 c Equation CORRELATION AND LINEAR REGRESSION 103 In multiple regression we are able to obtain an equation from which we are able to predict y from values of x1 x2 etc. and so develop an understanding of which variables are able to affect y This is a useful function for exploring complex relationships as within living systems it is unusual to find that an association is restricted to just two variables. Exercise The