Using this output interpret the results of our model. What do the coefficients t
ID: 2908485 • Letter: U
Question
Using this output interpret the results of our model.
What do the coefficients tell us?
How well can we predict weight using the height and Healthy Eating question?
How would you summarize this to a lay-person?
If we want to predict one of the teenagers weights we would want to know their height. This leads to the simple regression model of
where W is the weight and H is the height. However, we might be able to get a more accurate model if we know the answer they gave to the question of how much they value healthy eating. They rated this from 1-5 with 1 being they value it very low and 5 being very high.
Call there answer to this healthy eating question E. Then we have a model of the form:
where E is a categorical variable.
Running this model in R gives the following output:
Call:
lm(formula = Weight ~ Height + `Healthy eating`, data = yp)
Residuals:
Min 1Q Median 3Q Max
-24.287 -6.068 -1.002 4.874 55.267
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -118.09625 5.65601 -20.880 <2e-16 ***
Height 1.06415 0.03157 33.703 <2e-16 ***
`Healthy eating`2 -0.61215 1.30447 -0.469 0.639
`Healthy eating`3 0.06681 1.11657 0.060 0.952
`Healthy eating`4 -0.67990 1.19490 -0.569 0.569
`Healthy eating`5 -1.81542 1.69824 -1.069 0.285
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.156 on 970 degrees of freedom
(13 observations deleted due to missingness)
Multiple R-squared: 0.5435, Adjusted R-squared: 0.5411
F-statistic: 231 on 5 and 970 DF, p-value: < 2.2e-16
Explanation / Answer
1.
Residuals:
Min 1Q Median 3Q Max
-24.287 -6.068 -1.002 4.874 55.267
Explanation: Residuals are the difference between the actual response values and the predicted response values by the model. R gives the 5 point summary of residuals, minimum, 1st quartile, median, 3rd quartile and the maximum value.
.
lm(formula = Weight ~ Height + `Healthy eating`, data = yp)
Explanation: This is the regression equation of the model where 'Weight' is the dependent variable and 'Height' and 'Eating habits' are the independent variables of the model.
.
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -118.09625 5.65601 -20.880 <2e-16 ***
## Height 1.06415 0.03157 33.703 <2e-16 ***
## `Healthy eating`2 -0.61215 1.30447 -0.469 0.639
## `Healthy eating`3 0.06681 1.11657 0.060 0.952
## `Healthy eating`4 -0.67990 1.19490 -0.569 0.569
## `Healthy eating`5 -1.81542 1.69824 -1.069 0.285
Explanation: The coefficient summary gives the least square estime of each independent variable and the test result for the significance of the coefficient slope and the intercept.
From the coefficient result summary,
The estimate of intercept is -11.09625 and it is significant at the 99.9% level of confidence ( 0.001% significance level, ***P< 0.001)
The coefficient Height is 1.06415 which mean the dependent variable will change 1.06415 for one unit change in height and it is significant at the 99.9% level of confidence ( 0.1% significance level, ***P< 0.001)
While the other independent variables, the eating habits such that `Healthy eating`2 , `Healthy eating`3 , `Healthy eating`4 and `Healthy eating`5 and not significant because the P-value is greater than 0.1 at 10% significance level.
.
## Residual standard error: 15.38 on 48 degrees of freedom
## Multiple R-squared: 0.6511, Adjusted R-squared: 0.6438
## F-statistic: 89.57 on 1 and 48 DF, p-value: 1.49e-12
Explanation:
The Residual Standard error gives the the standard deviation of the residuals which indicates the quality of fit of the model.
The multiple R-squared value is 0.5435 which means IV explains the 54.35% of the variance of DV. This percentage indicates how well the model fit the data points.
The F-statistic indicates whether there is a relationship between the dependent and independent variables. The F-statistic of the model = 231 and p-value for F-statistic is approximately zero. The P-value is less than 0.001 at 0.1% significance level which is sufficient to reject the null hypothesis (H0 : There is no relationship between dependent and independent variables).
Conclusion: Based on the regression analysis we can state that the regression model explains the 54.35% of the variance of weight while only height is a good predictor variable of Weight.
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