I have a data set above, but need an explanation if the data is liner and depend

Question

I have a data set above, but need an explanation if the data is liner and dependent.

I am hoping to predict Active Power based on the temperature do you think I can show this from this data?

Based on the Linear fit and summary of fit what is the data actually stating. with the RSquare, RSquare ADJ, Prob>F, Prob > t, and the Bivariate NOrmal correlation signif .Prob?

-Fit Group Bivariate Fit of CT11ACTIVE POWER By CT11 AVRG TEMP B/F PRE-FILTER 160 140 u 120 100 80 60 40 20 30 35 40 45 50 55 60 65 70 75 80 CT11 AVRG TEMP B/F PRE-FILTER v-Linear Fit -Bivariate Normal Ellipse P=0.990 Linear Fit CT11ACTIVE POWER 171.56256 - 0.4100065 CT11 AVRG TEMP B/ F PRE-FILTER Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.045402 0.043977 19.59067 149.4237 672 Lack Of Fit Sum of Source Lack Of Fit 532 227194.93 Pure Error 138 29947.40 Total Error 670 257142.33 DF Squares Mean Square F Ratio 427.058 1.9679 217.010 Prob> F F ,0001* Parameter Estimates Term Intercept CT11 AVRG TEMP B/F PRE-FILTER -0.410006 0.072632-5.64 171.56256 3.994007 42.95

Explanation / Answer

There are data related to two regression analysis

The first one is Active power & average temperature

For this model , the data is not linear. This is because the regression model has a r square that is very close to Zero.

r square = 0.0454

r square adj= 0.0439

.

A value of r square close to zero implies that the correlation is very weak

A value of r square adj = 0.0439 means only 0.0439 *100 = 4.39% of the variation in active power is explained by Average temperature.

Thus we do not find the linear model to fit this data

In the table of bivariate model , we find that correlation value is 0.952459

This value implies that the bivariate model shows a stronger relation.

Thus we consider that the first set of variables do not share a linear relation , but Active power is surely dependent on Avg temperature as per the bivariate model.

.

The second model deals with active power and normalized load.4

We find that for the linear model it has r square 0.9071 , this means 90.71% of the variation is active power is explained by normalized load.

Thus they share a linear relation and yes active power is dependent on normalized load.

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