Question

1. It has been established for a long time that height has a positive correlation with weight. As people gets taller their weight increases. In a research study, a linear regression model was proposed to predict weight based on height. R output below provides the analysis. Interpret it, list any strengths and limitations of the result.

Call:

lm(formula = Weight ~ Height)

Residuals:

    Min      1Q Median      3Q     Max

-6.7104 -2.9217 0.4276 2.3973 7.8586

Coefficients:

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

(Intercept) 44.4545    18.7277   2.374 0.02894 *

Age              1.3310       0.5849 2.276 0.02257 *

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.195 on 18 degrees of freedom

Multiple R-squared: 0.5344,    Adjusted R-squared: 0.503

F-statistic: 13.82 on 1 and 18 DF, p-value: 0.01574

Answer 1

As the result shows the correlation is 0.5344,

So we can say weight are height are positively correlated and the correlation of determination is 0.503, by that we can say only 50.3% of variablity of weight is explained by the regression line.

We take significance level is 0.05,

We can say that all the height and weight are significantly related. As p-value <0.05