I am trying to determine if there is a relationship between a dependent variable y and independent variable x by fitting a least squares regression model.
The residuals seem to have constant variance, and there isn't any clear pattern in the residual vs fitted plot. However, the R-squared and the significance of the model fit's coefficients are very low. In this case, are there any nonlinearity issues that needs to be remediated with a transformation or can I conclude that my model is adequate with the correct functional form ?
Here is the summary of the model:
lm(formula = y ~ x, data = data) Residuals: Min 1Q Median 3Q Max -331911 -235678 -145867 30576 1749376 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.440e+05 7.037e+04 3.468 0.00135 ** x 1.796e-04 6.206e-04 0.289 0.77385 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 390100 on 37 degrees of freedom Multiple R-squared: 0.002259, Adjusted R-squared: -0.02471 F-statistic: 0.08378 on 1 and 37 DF, p-value: 0.7739