Multiple Linear Regression - Estimated Regression Equation
DE[t] = + 33.3249 + 0.491587`Solids,`[t] + 0.00123242`Osmo,`[t] -0.0262518t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+33.33 4.257+7.8270e+00 2.042e-08 1.021e-08
`Solids,`+0.4916 0.6357+7.7330e-01 0.446 0.223
`Osmo,`+0.001232 0.01534+8.0320e-02 0.9366 0.4683
t-0.02625 0.0237-1.1080e+00 0.2777 0.1388


Multiple Linear Regression - Regression Statistics
Multiple R 0.5711
R-squared 0.3262
Adjusted R-squared 0.2513
F-TEST (value) 4.357
F-TEST (DF numerator)3
F-TEST (DF denominator)27
p-value 0.01258
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 1.172
Sum Squared Residuals 37.07


Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1 44.5 43.51 0.9915
2 44.3 43.64 0.6628
3 44.2 43.97 0.2339
4 42.3 44.16-1.858
5 42.6 43.77-1.166
6 42.4 43.41-1.01
7 42.9 43.3-0.4006
8 44 43.49 0.5105
9 43.5 42.87 0.6269
10 44.8 44.19 0.6069
11 43.9 44.12-0.2163
12 43.6 43.2 0.3951
13 42.1 43.2-1.102
14 43 43.67-0.6688
15 42 42.82-0.8189
16 43.8 42.93 0.8672
17 45.2 43.39 1.813
18 45 43.59 1.412
19 44.7 42.84 1.861
20 43.4 43.13 0.2736
21 44.4 43.57 0.8252
22 42.9 42.83 0.07178
23 42.3 43.66-1.359
24 43.3 43.52-0.2181
25 41.5 42.85-1.353
26 39 39.74-0.7385
27 42.2 43.22-1.018
28 43.95 42.89 1.064
29 41.2 43.67-2.473
30 45.3 43.56 1.744
31 43.4 42.96 0.4418


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
7 0.03674 0.07347 0.9633
8 0.1709 0.3418 0.8291
9 0.08745 0.1749 0.9126
10 0.4008 0.8016 0.5992
11 0.2774 0.5548 0.7226
12 0.1776 0.3551 0.8224
13 0.1796 0.3592 0.8204
14 0.1349 0.2698 0.8651
15 0.1181 0.2362 0.8819
16 0.1106 0.2212 0.8894
17 0.1531 0.3062 0.8469
18 0.1344 0.2688 0.8656
19 0.1644 0.3288 0.8356
20 0.1137 0.2275 0.8863
21 0.1007 0.2014 0.8993
22 0.08797 0.1759 0.912
23 0.0703 0.1406 0.9297
24 0.05371 0.1074 0.9463


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level0 0OK
5% type I error level00OK
10% type I error level10.0555556OK


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 0.90321, df1 = 2, df2 = 25, p-value = 0.4181
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 0.67924, df1 = 6, df2 = 21, p-value = 0.668
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 0.98183, df1 = 2, df2 = 25, p-value = 0.3886


Variance Inflation Factors (Multicollinearity)
> vif
`Solids,`   `Osmo,`         t 
15.466179 15.411955  1.014185