I have the following information:
Height Weight
170 65
167 55
189 85
175 70
166 55
174 55
169 69
170 58
184 84
161 56
170 75
182 68
167 51
187 85
178 62
173 60
172 68
178 55
175 65
176 70
I want to construct quadratic and cubic regression analysis in Excel. I know how to do it by linear regression in Excel, but what about quadratic and cubic? I have searched a lot of resources, but could not find anything helpful.
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excel
regression
I know that this question is a little old, but I thought that I would provide an alternative which, in my opinion, might be a little easier. If you're willing to add "temporary" columns to a data set, you can use Excel's Analysis ToolPak?Data Analysis?Regression. The secret to doing a quadratic or a cubic regression analysis is defining the Input X Range:.
If you're doing a simple linear regression, all you need are 2 columns, X & Y. If you're doing a quadratic, you'll need X_1, X_2, & Y where X_1 is the x variable and X_2 is x^2; likewise, if you're doing a cubic, you'll need X_1, X_2, X_3, & Y where X_1 is the x variable, X_2 is x^2 and X_3 is x^3. Notice how the Input X Range is from A1 to B22, spanning 2 columns.
The following image the output of the regression analysis. I've highlighted the common outputs, including the R-Squared values and all the coefficients.
The LINEST function described in a previous answer is the way to go, but an easier way to show the 3 coefficients of the output is to additionally use the INDEX function. In one cell, type: =INDEX(LINEST(B2:B21,A2:A21^{1,2},TRUE,FALSE),1) (by the way, the B2:B21 and A2:A21 I used are just the same values the first poster who answered this used... of course you'd change these ranges appropriately to match your data). This gives the X^2 coefficient. In an adjacent cell, type the same formula again but change the final 1 to a 2... this gives the X^1 coefficient. Lastly, in the next cell over, again type the same formula but change the last number to a 3... this gives the constant. I did notice that the three coefficients are very close but not quite identical to those derived by using the graphical trendline feature under the charts tab. Also, I discovered that LINEST only seems to work if the X and Y data are in columns (not rows), with no empty cells within the range, so be aware of that if you get a #VALUE error.
Source: Stackoverflow.com