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Rstudio programming (R programming) The weight and systolic blood pressure of 26 randomly selected males in...

(R programming) The weight and systolic blood pressure of 26 randomly selected males in the age group 25-30 are found in the

| AB weight_sys bp 165 130 167 133 180 150 128 151 146 150 175 190 210 140 200 148 in no-mio- 158 169 170 172 159 174 183 215

180| 143 240 235 192 187 156 124 170 165 160 159

Rstudio programming

(R programming) The weight and systolic blood pressure of 26 randomly selected males in the age group 25-30 are found in the attached CSV file. Fit a simple linear regression model relating systolic blood pressure (y) to weight (2). (30 points) (a) Provide the R code which fits the model and outputs the summary of the fitting. (b) Report the model fitting summary (c) Write down the fitted linear model and its interpretation. (d) Write down the null and alternative hypotheses for testing the slope, B1. Draw a conclusion based on the observed test statistic and p-value.
| AB weight_sys bp 165 130 167 133 180 150 128 151 146 150 175 190 210 140 200 148 in no-mio- 158 169 170 172 159 174 183 215 195 150 163
180| 143 240 235 192 187 156 124 170 165 160 159
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Answer #1

a)

R code

® RStudio File Edit Code - OR View Plots Build Session O Debug Profile Tools Go to file/function Help 69 - Addins - H Project

b)

R-output Model fitting summary

Version:1.0 StartHTML:0000000107 EndHTML:0000002858 StartFragment:0000000127 EndFragment:0000002840

> summary(fit)

Call:
lm(formula = sys_bp ~ weight)

Residuals:
    Min      1Q  Median      3Q     Max 
-17.182  -6.485  -2.519   8.926  12.143 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 69.10437   12.91013   5.353 1.71e-05 ***
weight       0.41942    0.07015   5.979 3.59e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.681 on 24 degrees of freedom
Multiple R-squared:  0.5983,    Adjusted R-squared:  0.5815 
F-statistic: 35.74 on 1 and 24 DF,  p-value: 3.591e-06

c)

Fitted linear regression model is

sys_bp =69.10437 + 0.41942 * weight

Interpretation :The Values of multiple R-squared: 0.5983 and Adjusted R-squared: 0.5815 are not closed to 1 so we can conclude that fitted model is not good linear fit between sys_bp and weight.

d)

Ho : B1 =0 ie. weight is not significant to predict sys_bp

VS

H1 : B1 \neq 0 i.e. weight is statistically significant.

P-value : 3.59e-06 = 0.00000359 < 0.05

   so we reject null hypothesis (H0)

Conclusion : B1 \neq 0 so weight is statistically significant with \alpha =0.05

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