Linear Regression Diagnostics
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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.
Scatterplot of data:
Diagnostic plots:
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
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
asked Nov 23 at 8:44
joe
61
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joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
1
down vote
favorite
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.
Scatterplot of data:
Diagnostic plots:
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
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
asked Nov 23 at 8:44
joe
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
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.
Scatterplot of data:
Diagnostic plots:
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
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
asked Nov 23 at 8:44
joe
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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.
Scatterplot of data:
Diagnostic plots:
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
statistics regression data-analysis linear-regression regression-analysis
statistics regression data-analysis linear-regression regression-analysis
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
asked Nov 23 at 8:44
joe
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
asked Nov 23 at 8:44
joe
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
edited Nov 23 at 9:10
Jean-Claude Arbaut
14.9k63362
14.9k63362
asked Nov 23 at 8:44
joe
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 23 at 8:44
joe
61
asked Nov 23 at 8:44
joe
61
61
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
joe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday
add a comment |
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday
add a comment |
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joe is a new contributor. Be nice, and check out our Code of Conduct.
joe is a new contributor. Be nice, and check out our Code of Conduct.
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The scatter plot shows the relation is not clearly linear, and accordingly the p-value for $x$ would lead to remove the variable from the model. I'd say the variability is not well explained by $x$ and you should look for other regressors. Also, the $R^2$ is far too low, which means the model explains only a small fration of the variance of $y$.
– Jean-Claude Arbaut
Nov 23 at 9:02
I completely agree with Jean-Claude Arbaut.
– Adrian Keister
yesterday