I want to do an exponential regression with this data in order to compare with linear and polynomial model.

TEMPERATURE;GAZ

8;1290

8;1340

10;1474

11;777

18;397

22;263

21;370

18;578

14;444

7;2478

6;3201

4;3330

8;2518

8;2306

12;1635

14;369

17;458

21;315

23;336

19;442

11;1062

9;2450

5;3088

2;3945

6;3070

6;2594

9;1705

11;398

19;369

19;261

19;379

17;371

11;339

6;2219

4;3044

2;2850

6;2584

9;1630

11;1174

17;337

21;293

23;337

**My results for the linear model :**

Call:

lm(formula = GAZ ~ TEMPERATURE, data = edf)

Residuals:

Min 1Q Median 3Q Max

-1251.29 -278.31 84.01 364.99 919.76

##
Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 3344.1 183.3 18.25 < 2e-16 ***

TEMPERATURE -159.4 13.4 -11.90 1.02e-14 ***

Signif. codes: 0 β* β 0.001 ββ 0.01 β*β 0.05 β.β 0.1 β β 1

Residual standard error: 538.7 on 40 degrees of freedom

Multiple R-squared: 0.7797, Adjusted R-squared: 0.7742

F-statistic: 141.6 on 1 and 40 DF, p-value: 1.021e-14

**My results for the polynomial model :**

lm(formula = GAZ ~ TEMPERATURE + I(TEMPERATURE^2), data = edf)

Residuals:

Min 1Q Median 3Q Max

-1026.93 -82.48 40.43 135.98 798.55

##
Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 4706.316 279.455 16.841 < 2e-16 ***

TEMPERATURE -436.194 50.380 -8.658 1.28e-10 ***

I(TEMPERATURE^2) 10.752 1.917 5.607 1.82e-06 ***

Signif. codes: 0 β* β 0.001 ββ 0.01 β*β 0.05 β.β 0.1 β β 1

Residual standard error: 406 on 39 degrees of freedom

Multiple R-squared: 0.878, Adjusted R-squared: 0.8718

F-statistic: 140.4 on 2 and 39 DF, p-value: < 2.2e-16

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