### Adv Data Science using R Quiz and Assignment 2

**These are Advance Data Science Using R Assignment 2 Solution**

## Quiz

**Q1. It helps to find a numerical value expressing the relationship** **between variables**

Regression

Correlation

Random Variable

Z-Value

**Answer: Correlation**

**Q2. It is used to estimate values of random variable on the** **basis of the values of fixed variable.**

Regression

Correlation

Random Variable

Z-Value

**Answer: Regression**

**Q3. It attempts to model the relationship between two variables by fitting a linear equation to observed data.**

Linear Regression

Covariance

Dependent Variable

S.D

**Answer: Linear Regression**

**These are Advance Data Science Using R Assignment 2 Solution**

**Q4. __________ prints out the function call stack after an error occurs.**

trace()

traceback()

back()

traback()

**Answer: traceback()**

**Q5. Linear regression uses_______ for graphical representation in determining the strength of the relationship between two variables.**

Histogram

Pie chart

Scatter diagram

Anova

**Answer: Scatter diagram**

**Q6. Which of the following is primary tool for debugging?**

debug()

trace()

browser()

traceback()

**Answer: debug()**

**These are Advance Data Science Using R Assignment 2 Solution**

**Q7. Point out the wrong statement?**

The primary task of debugging any R code is correctly diagnosing what the problem is

R provides only two tools to help you with debugging your code

print statement can be used for debugging purpose

The traceback() function must be called immediately after an error occurs

**Answer: R provides only two tools to help you with debugging your code**

**Q8. Which function will be used melt.mind2<-_______(mind, id=c(“ID”,”BTW”)) melt.mind2**

Cast

Melt

melt

cast

**Answer: melt**

**Q9. Which function combines vectors as columns?**

rbind()

cbind()

merge()

none of the above

**Answer: cbind()**

**These are Advance Data Science Using R Assignment 2 Solution**

**Q10. The slope of the regression line of Y on X is also referred to as the:**

Regression coefficient of X on Y

The correlation coefficient of X on Y

Regression coefficient of Y on X

Correlation coefficient of Y on X.

**Answer: Regression coefficient of Y on X**

**Q11. Which of the assertions below is the least accurate?**

When outliers are present in the data series, correlation is a more reliable or relevant measure.

Two variables having a significant nonlinear relation can still have a relatively low correlation.

Correlation among two variables can emerge from their relationship with a third variable rather than a direct relationship between them.

None of the preceding.

**Answer: When outliers are present in the data series, correlation is a more reliable or relevant measure.**

**Q12. The correlation coefficient is?**

The square of the coefficient of determination

Can never be negative

The square root of the coefficient of determination.

The same as r square

**Answer: The square root of the coefficient of determination.**

**These are Advance Data Science Using R Assignment 2 Solution**

**Q13. The correlation for the values of two variables moving in the same direction is**

Perfect positive

Negative

Positive

No correlation.

**Answer: Positive**

**Q14. Who introduced the term ‘regression’?**

Karl Pearson

R.A Fischer

Croxton and Cowden

Francis Galton.

**Answer: Francis Galton.**

**Q15. The correlation coefficient describes**

Only magnitude

Both magnitude and direction

Only direction

None of the preceding options.

**Answer: Both magnitude and direction**

**These are Advance Data Science Using R Assignment 2 Solution**

## Assignment

**Q1) Do the data visualization by using regression in R.**

**Solution:**

**Please update your NAME and UID in every code and then paste ss.**

### Step 1: Download both sample datasets

Start by downloading R and RStudio. Then open RStudio and click on **File > New File > R Script**.

To install the packages you need for the analysis, run this code (you only need to do this once):

`install.packages("ggplot2")`

install.packages("dplyr")

install.packages("broom")

install.packages("ggpubr")

Next, load the packages into your R environment by running this code (you need to do this every time you restart R):

`library(ggplot2)`

library(dplyr)

library(broom)

library(ggpubr)

### Step 2: Load the data into R

Follow these four steps for each dataset:

- Extract the Downloaded Zip of sample datasets.
- In RStudio, go to
**File > Import dataset > From Text (base)**. - Choose the data file you have downloaded (income.csv or heart.csv), and an
**Import Dataset**window pops up. - In the
**Data Frame**window, you should see an**X**(index) column and columns listing the data for each of the variables (income and happiness or biking, smoking, and heart.disease). - Click on the
**Import**button and the file should appear in your**Environment**tab on the upper right side of the RStudio screen.

After you’ve loaded the data, check that it has been read in correctly using `summary()`

.

### Step 3: Perform the linear regression analysis

### Simple regression: income and happiness

```
income.happiness.lm <- lm(happiness ~ income, data = income.data)
summary(income.happiness.lm)
print("Name: PROGIES ,UID:")
```

The output looks like this:

### Multiple regression: biking, smoking, and heart disease

```
heart.disease.lm<-lm(heart.disease ~ biking + smoking, data = heart.data)
summary(heart.disease.lm)
print("Name: PROGIES ,UID:")
```

The output looks like this:

### Step 4: Check for homoscedasticity

### Simple regression

```
par(mfrow=c(2,2))
plot(income.happiness.lm)
par(mfrow=c(1,1))
```

print("Name: PROGIES ,UID:")

These are the residual plots produced by the code:

### Multiple regression

```
par(mfrow=c(2,2))
plot(heart.disease.lm)
par(mfrow=c(1,1))
```

print("Name: PROGIES ,UID:")

The output looks like this:

### Step 5: Visualize the results with a graph

### Simple regression

Follow 4 steps to visualize the results of your simple linear regression.

**Plot the data points on a graph**

```
income.graph<-ggplot(income.data, aes(x=income, y=happiness))+
geom_point()
income.graph
print("Name: PROGIES ,UID:")
```

**Add the linear regression line to the plotted data**

```
income.graph <- income.graph + geom_smooth(method="lm", col="black")
income.graph
print("Name: PROGIES ,UID:")
```

**Add the equation for the regression line.**

```
income.graph <- income.graph +
stat_regline_equation(label.x = 3, label.y = 7)
income.graph
print("Name: PROGIES ,UID:")
```

**Make the graph ready for publication**

```
income.graph +
theme_bw() +
labs(title = "Reported happiness as a function of income",
x = "Income (x$10,000)",
y = "Happiness score (0 to 10)")
print("Name: PROGIES ,UID:")
```

This produces the finished graph that you can include in your papers:

### Multiple regression

There are 7 steps to follow.

**Create a new dataframe with the information needed to plot the model**

```
plotting.data<-expand.grid(
biking = seq(min(heart.data$biking), max(heart.data$biking), length.out=30),
smoking=c(min(heart.data$smoking), mean(heart.data$smoking), max(heart.data$smoking)))
print("Name: PROGIES ,UID:")
```

**Predict the values of heart disease based on your linear model**

```
plotting.data$predicted.y <- predict.lm(heart.disease.lm, newdata=plotting.data)
print("Name: PROGIES ,UID:")
```

**Round the smoking numbers to two decimals**

```
plotting.data$smoking <- round(plotting.data$smoking, digits = 2)
print("Name: PROGIES ,UID:")
```

**Change the ‘smoking’ variable into a factor**

```
plotting.data$smoking <- as.factor(plotting.data$smoking)
print("Name: PROGIES ,UID:")
```

**Plot the original data**

```
heart.plot <- ggplot(heart.data, aes(x=biking, y=heart.disease)) +
geom_point()
heart.plot
print("Name: PROGIES ,UID:")
```

**Add the regression lines**

```
heart.plot <- heart.plot +
geom_line(data=plotting.data, aes(x=biking, y=predicted.y, color=smoking), size=1.25)
heart.plot
print("Name: PROGIES ,UID:")
```

**Make the graph ready for publication**

```
heart.plot <-
heart.plot +
theme_bw() +
labs(title = "Rates of heart disease (% of population) \n as a function of biking to work and smoking",
x = "Biking to work (% of population)",
y = "Heart disease (% of population)",
color = "Smoking \n (% of population)")
heart.plot
print("Name: PROGIES ,UID:")
```

```
heart.plot + annotate(geom="text", x=30, y=1.75, label=" = 15 + (-0.2*biking) + (0.178*smoking)")
print("Name: PROGIES ,UID:")
```

This is the finished graph that you can include in your papers!

### Step 6: Report your results

In addition to the graph, include a brief statement explaining the results of the regression model.Reporting the results of simple linear regressionWe found a significant relationship between income and happiness (*p* < 0.001, *R*^{2} = 0.73 ± 0.0193), with a 0.73-unit increase in reported happiness for every $10,000 increase in income.Reporting the results of multiple linear regressionIn our survey of 500 towns, we found significant relationships between the frequency of biking to work and the frequency of heart disease and the frequency of smoking and frequency of heart disease (*p* < 0 and *p* < 0.001, respectively).

Specifically we found a 0.2% decrease (± 0.0014) in the frequency of heart disease for every 1% increase in biking, and a 0.178% increase (± 0.0035) in the frequency of heart disease for every 1% increase in smoking.

**Q2) Fill appropriate debugging function into the blank space.**

- A more sophisticated debugging method is to put a call to
**browser()**in your code. This will stop execution at that point and open R’s interactive debugger. In the debugger you can run any R command to look at objects in the current environment, modify them and continue executing. - The
**traceback()**function can be used to print a summary of how your program arrived at the error. This is also called a call stack. In R this gives you each call that lead up to the error, which can be very useful for determining what lead to the error. **recover()**is not used directly, instead it is used as an error handler, by calling options(error =**recover**). You can also use other functions, such as browser() as an error handler, which will start the debugger automatically when there is an error.

**Q3) Write the code to reshape the following data first from wide to long and then long to wide. Write the name of the functions you will use.**

**Solution:**

Wide to long:

```
import pandas as pd
# Create wide dataframe
df = pd.DataFrame({'id': [1, 1, 2, 2], 'time': [1, 2, 1, 2], '*1': [5, 3, 6, 2], '*2': [6, 5, 1, 4]})
# Use pd.melt() to reshape data
df_long = pd.melt(df, id_vars=['id', 'time'], value_vars=['*1', '*2'], var_name='variable', value_name='value')
```

Long to wide:

```
# Use pd.pivot_table() to reshape data
df_wide = df_long.pivot_table(index=['id', 'time'], columns='variable', values='value')
# Reset the index
df_wide.reset_index(inplace=True)
```

**These are Advance Data Science Using R Assignment 2 Solution**

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