Quiz & Assignment-2

QUIZ-2

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

• Regression

• Correlation

• Random Variable

• Z-Value

Correct 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

Correct 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

Correct Answer : Linear Regression

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

• trace()

• traceback()

• back()

• traback()

Correct 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

Correct Answer : Scatter diagram

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

• debug()

• trace()

• browser()

• traceback()

Correct Answer : debug()

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

Correct 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

Correct Answer : melt

Q9. Which function combines vectors as columns?

• rbind()

• cbind()

• merge()

• none of the above

Correct Answer : cbind()

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.

Correct 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.

Correct 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

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

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

• Perfect positive

• Negative

• Positive

• No correlation.

Correct Answer : Positive

Q14. Who introduced the term ‘regression’?

• Karl Pearson

• R.A Fischer

• Croxton and Cowden

• Francis Galton.

Correct Answer : Francis Galton.

Q15. The correlation coefficient describes

Only magnitude

Both magnitude and direction

Only direction

None of the preceding options.

Correct Answer : Both magnitude and direction

Assignment-2

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

Answer :

Step 1: Download both sample datasets

 Simple regression dataset 

Multiple regression dataset

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:

1. Extract the Downloaded Zip of sample datasets.

2. In RStudio, go to File > Import dataset  > From Text (base).

3. Choose the data file you have downloaded (income.csv or heart.csv), and an Import Dataset window pops up.

4. 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).

5. 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: BRAINHEALERS ,UID:21BCS____")

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: BRAINHEALERS ,UID:21BCS____")

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: BRAINHEALERS ,UID:21BCS____")

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: BRAINHEALERS ,UID:21BCS____")

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.

1. Plot the data points on a graph

income.graph<-ggplot(income.data, aes(x=income, y=happiness))+geom_point()

income.graph

print("Name: BRAINHEALERS ,UID:21BCS____")

2. Add the linear regression line to the plotted data

income.graph <- income.graph + geom_smooth(method="lm", col="black")

income.graph

print("Name: BRAINHEALERS ,UID:21BCS____")

3. Add the equation for the regression line.

income.graph <- income.graph +

  stat_regline_equation(label.x = 3, label.y = 7)

income.graph

print("Name: BRAINHEALERS ,UID:21BCS____")

4. 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: BRAINHEALERS ,UID:21BCS____")

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

Multiple regression

There are 7 steps to follow.

1. 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: BRAINHEALERS ,UID:21BCS____")

2. 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: BRAINHEALERS ,UID:21BCS____")

3. Round the smoking numbers to two decimals

plotting.data$smoking <- round(plotting.data$smoking, digits = 2)

print("Name: BRAINHEALERS ,UID:21BCS____")

4. Change the ‘smoking’ variable into a factor

plotting.data$smoking <- as.factor(plotting.data$smoking)

print("Name: BRAINHEALERS ,UID:21BCS____")

5. Plot the original data

heart.plot <- ggplot(heart.data, aes(x=biking, y=heart.disease)) +

  geom_point()

heart.plot

print("Name: BRAINHEALERS ,UID:21BCS____")

6. 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: BRAINHEALERS ,UID:21BCS____")

7. 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: BRAINHEALERS ,UID:21BCS____")

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

print("Name: BRAINHEALERS ,UID:21BCS____")

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, R2 = 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.

1. 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.

2. 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.

3. 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)