Question

1. Consider the dataset in the proj2-3.txt file on BlackBoard. In this problem, focus is on high systolic blood pressure (sbp) and possible explanatory variables Body Mass Index (bmi), and scale (scl). Consider the linear regression model with response high SBP and scale as explana- tory variables.

Explain the coefficients in the model?
Explain the null hypotheses that the estimated slope equals 0?

Write a summary of your findings. What is your conclusion?

Residuals:
Min 1Q Median 3Q Max
-72.64 -27.55 -5.95 23.80 319.53

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 133.9896 18.6598 7.181 4.23e-12 ***
SBP 0.5961 0.1531 3.893 0.000119 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 40.4 on 348 degrees of freedom
Multiple R-squared: 0.04173,   Adjusted R-squared: 0.03897
F-statistic: 15.15 on 1 and 348 DF, p-value: 0.0001188

Answer 1

The output you have shared is not complete, the explanatory variables Body Mass Index (bmi), and scale (scl) are missing from the output. It has SBO which is a dependent variable that should not be in this output. Please check or provide the data set Therefore, we cannot explain the coefficients but I am sharing how you can do it. For example, say the bmi coefficient(estimate) is 0.5961 that means if there is a unit increase in bmi then sbp will increase by an amount of 0.5961 You can use this explanation to explain the coefficients in the correct model. The null and alternative hypotheses to test slope of first explanatory varibl If the p-value is less than the level of significance say 500, we reject the null hypothesis and conclude that the explanatory variable is significantly related to the dependent variable. The final conclusion is based on the p-value of the whole model which is 0.0001188 in the given output so we can say that the model is significant because it is less than 5%. If you have any doubts then please let me know in comments