Look at the code for the section below to see how to programmatically (i.e., automatically) grab the coefficient values from the output and have them print in your document.
The intercept (b_0) was 146.194, t(1) = 31.995, p < .0001. An individual who did not have an infection and had a non-emergency admission is expected to have blood pressure of 146.194.
The slope for Infection (b_1) was -13.553, t(1) = -2.927, p<.01. Holding Emergency constant, the difference between in blood pressure between an infection and a non-infection patient is -13.553 points. Patients with an infection have lower blood pressure.
The slope for Emergency (b_2) was -11.186, t(1) = -2.160, p<.05. Holding Infection constant, the difference between in blood pressure between an emergency admit and a non-emergency admit patient is -11.186 points. Patients with an emergency admission have lower blood pressure.
Based on model 3, what are the predicted blood pressures for the 4 combinations of infection status and admission type? (i.e., infected non-emergency, non-infected non-emergency, infected emergency, non-infected emergency)
Using the predicted and residual values, assess whether the assumptions are met for model 3. Include the plots and describe your conclusions based on them.
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: reciprocal condition number 0
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: There are other near singularities as well. 1.01
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used at
-0.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius
1.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : reciprocal condition
number 0
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : There are other near
singularities as well. 1.01
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: reciprocal condition number 0
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: There are other near singularities as well. 1.01
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used at
-0.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius
1.005
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : reciprocal condition
number 0
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : There are other near
singularities as well. 1.01
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: reciprocal condition number 1.4154e-14
Warning in simpleLoess(y, x, w, span, degree = degree, parametric = parametric,
: There are other near singularities as well. 183.69
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : pseudoinverse used at
121.33
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : neighborhood radius
13.677
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : reciprocal condition
number 1.4154e-14
Warning in predLoess(object$y, object$x, newx = if (is.null(newdata)) object$x
else if (is.data.frame(newdata))
as.matrix(model.frame(delete.response(terms(object)), : There are other near
singularities as well. 183.69
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
In plain language, answer the research question: How do infection status and admission type predict blood pressure? (This should not be lengthy – just a couple sentences.)
Source Code
---title: "BTS 510 Lab 7"format: html: embed-resources: true self-contained-math: true html-math-method: katex number-sections: true toc: true code-tools: true code-block-bg: true code-block-border-left: "#31BAE9"---```{r}#| label: setupset.seed(12345)library(tidyverse)library(Stat2Data)theme_set(theme_classic(base_size =16))```## Learning objectives* **Add predictors** to a linear regression model* Interpret **partial regression coefficients*** **Re-code predictors** to answer your research questions* **Compare** different models using $R^2_{change}$## Data * `ICU` data from the **Stat2Data** package * `ID`: Patient ID code * `Survive`: 1 = patient survived to discharge or 0 = patient died * `Age`: Age (in years) * `AgeGroup`: 1 = young (under 50), 2 = middle (50-69), 3 = old (70+) * `Sex`: 1 = female or 0 = male * `Infection`: 1 = infection suspected or 0 = no infection * `SysBP`: Systolic blood pressure (in mm of Hg) * `Pulse`: Heart rate (beats per minute) * `Emergency`: 1 = emergency admission or 0 = elective admission## Research question**How do infection status (`Infection`) and admission type (`Emergency`) predict blood pressure?**## Tasks```{r}library(Stat2Data)data(ICU)```1. Conduct **three linear regression models** to address the above research questions.* Model 1: Infection status predicts blood pressure* Model 2: Admission type predicts blood pressure* Model 3: Infection status *and* admission type predict blood pressure```{r}m1 <-lm(data = ICU, SysBP ~ Infection)m2 <-lm(data = ICU, SysBP ~ Emergency)m3 <-lm(data = ICU, SysBP ~ Infection + Emergency)``````{r}summary(m1)summary(m2)summary(m3)library(modelsummary)modelsummary(list(m1, m2, m3))``````{r}cor(ICU[, c(6, 7, 9)])```2. **Which is the best model?** * Use the $F$-test for $R^2_{change}$ and the AIC values to help you decide. Report the tests and values that you used to decide this. ```{r}anova(m3, m1)anova(m3, m2)AIC(m1)AIC(m2)AIC(m3)```3. Report the results of the **best** model, including: * Intercept value, test statistic, $p$-value, interpretation (in words) * Slope value(s), test statistic(s), $p$-value(s), interpretation(s) (in words) * $R^2$ value, test statistic, $p$-value, interpretation (in words)```{r}m3_coeff <-summary(m3)$coefficientsm3_coeff```::: {.callout-note}Look at the code for the section below to see how to programmatically (i.e., automatically) grab the coefficient values from the output and have them print in your document. :::* $\hat{SysBP} = `r round(m3_coeff[1], 3)` + `r round(m3_coeff[2], 3)` \times Infection + `r round(m3_coeff[3], 3)` \times Emergency$* The intercept ($b_0$) was `r round(m3_coeff[1], 3)`, t(1) = 31.995, p < .0001. An individual who did not have an infection and had a non-emergency admission is expected to have blood pressure of `r round(m3_coeff[1], 3)`.* The slope for `Infection` ($b_1$) was `r round(m3_coeff[2], 3)`, t(1) = -2.927, p<.01. Holding `Emergency` constant, the difference between in blood pressure between an infection and a non-infection patient is `r round(m3_coeff[2], 3)` points. Patients with an infection have lower blood pressure.* The slope for `Emergency` ($b_2$) was `r round(m3_coeff[3], 3)`, t(1) = -2.160, p<.05. Holding `Infection` constant, the difference between in blood pressure between an emergency admit and a non-emergency admit patient is `r round(m3_coeff[3], 3)` points. Patients with an emergency admission have lower blood pressure.4. Based on **model 3**, what are the predicted blood pressures for the 4 combinations of infection status and admission type? (i.e., infected non-emergency, non-infected non-emergency, infected emergency, non-infected emergency)* Non-infected non-emergency```{r}summary(m3)$coefficients[1] +summary(m3)$coefficients[2] *0+summary(m3)$coefficients[3] *0```* Infected non-emergency```{r}summary(m3)$coefficients[1] +summary(m3)$coefficients[2] *1+summary(m3)$coefficients[3] *0```* Non-infected emergency```{r}summary(m3)$coefficients[1] +summary(m3)$coefficients[2] *0+summary(m3)$coefficients[3] *1```* Infected emergency```{r}summary(m3)$coefficients[1] +summary(m3)$coefficients[2] *1+summary(m3)$coefficients[3] *1```5. Using the **predicted** and **residual** values, assess whether the assumptions are met for **model 3**. Include the plots and describe your conclusions based on them. ```{r}ICU$pred <-fitted(m3)ICU$resi <-residuals(m3)``````{r}ggplot(data = ICU, aes(x = Infection, y = resi)) +geom_point(alpha =0.3, size =2) +geom_smooth()ggplot(data = ICU, aes(x = Emergency, y = resi)) +geom_point(alpha =0.3, size =2) +geom_smooth()ggplot(data = ICU, aes(x = pred, y = resi)) +geom_point(alpha =0.3, size =2) +geom_smooth()ggplot(data = ICU,aes(x = resi)) +geom_histogram()```6. In plain language, answer the research question: **How do infection status and admission type predict blood pressure?** (This should not be lengthy -- just a couple sentences.)
