Solution :
Explanation :
The regression Equation is;
Where "b0" is Intercept parameter and "b1" Slope parameter
Formulas for Intercept and slope parameters is;
Where X = time in a Day
Y = Height in Cm
So regression equation by using Excel calculation is ;
Time (days)(X) | Height (Y) | (X -Mean(X)) | (Y - Mean(Y)) | (X - Mean(X))^2 | (X -Mean(X))(Y -Mean(Y)) | |
1 | 0.1 | -5.5 | -1.416666667 | 30.25 | 7.791666667 | |
2 | 0.1 | -4.5 | -1.416666667 | 20.25 | 6.375 | |
3 | 0.3 | -3.5 | -1.216666667 | 12.25 | 4.258333333 | |
4 | 0.9 | -2.5 | -0.616666667 | 6.25 | 1.541666667 | |
5 | 1.2 | -1.5 | -0.316666667 | 2.25 | 0.475 | |
6 | 1.4 | -0.5 | -0.116666667 | 0.25 | 0.058333333 | |
7 | 1.8 | 0.5 | 0.283333333 | 0.25 | 0.141666667 | |
8 | 2 | 1.5 | 0.483333333 | 2.25 | 0.725 | |
9 | 2.2 | 2.5 | 0.683333333 | 6.25 | 1.708333333 | |
10 | 2.5 | 3.5 | 0.983333333 | 12.25 | 3.441666667 | |
11 | 2.7 | 4.5 | 1.183333333 | 20.25 | 5.325 | |
12 | 3 | 5.5 | 1.483333333 | 30.25 | 8.158333333 | |
Sum | 78 | 18.2 | 143 | 40 | ||
Mean | 6.5 | 1.516667 | ||||
b1 | 0.280 | |||||
b0 | -0.30152 | |||||
Regression Equation is : | ||||||
Y = -0.301 + 0.28 X |
Also If you have to predict the day 16th height then it is
cm
Excel Regression Output For reference):
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.99345748 | |||||||
R Square | 0.986957764 | |||||||
Adjusted R Square | 0.985653541 | |||||||
Standard Error | 0.121595838 | |||||||
Observations | 12 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 11.18881119 | 11.18881119 | 756.7397 | 9.34E-11 | |||
Residual | 10 | 0.147855478 | 0.014785548 | |||||
Total | 11 | 11.33666667 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -0.301515152 | 0.074837065 | -4.028954796 | 0.002404 | -0.46826 | -0.13477 | -0.46826 | -0.13477 |
Time (days)(X) | 0.27972028 | 0.010168355 | 27.50890243 | 9.34E-11 | 0.257064 | 0.302377 | 0.257064 | 0.302377 |
Let's not forget about regression! Let's say I'd like to make a prediction about how quickly...
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