AccelerateAI - Data Science Global Bootcamp - Assignment 05  - Solved

Simple Linear Regression

Q1: The Dean of a college wants to examine the effect of internship experience on marketability in the workplace. She takes a random sample of 4 students. For these 4, she finds out how many times each had an internship and how many job offers they received upon graduation. These data are presented in the table below.  

Student    Internship(s)     Job Offer

1                   1                          4  2                   2                         6

3                            1                         3   

4                            0                         1

 

1. What is the independent variable X?  

a)  Internship  

b)  Job Offers  

c)   Marketability in the workplace  

d)  None of the Above  

 

2. Referring to the above data, the estimate of the slope is  

 a) 0.4   b) 2    c) 2.50    d) 5

 

 

Q2: Score received on an exam measured in "percentage points" (Y) is regressed on “percentage attendance” (X) for 22 students in the course Statistics for Data Science.  If the Y intercept, b0 = 39.39 and the slope, b1 = 0.341, which of the following statement is correct?

 

a)    If attendance increases by 0.341%, the estimated average score received will increase by 1 percentage point.  

b)    If attendance increases by 1%, the estimated average score received will increase by 39.39 percentage points.  

c)    If attendance increases by 1%, the estimated average score received will increase by 0.341 percentage points.  

d)    If the score received increases by 39.39%, the estimated average attendance will go up by 1%.

 

 

Q3. A survey was conducted to see if a relation exists between expenditure on higher education (X), and Salary growth in percentage (Y).  The result obtained is summarized in the table. Write down the regression equation.

  

 

 

 

Q4. A model was built to determine how crime rate in the neighbourhood impacts property prices in USA. The incomplete coefficient table is shown below.

Calculate the rate at which the property price changes for unit change in the Crime Rate (CRIM).

  

 

 

 

 

Q5. Ajishek Bacchan, researcher at GharDekho.com claims that for every unit increase in crime rate, the price will decrease by at least INR 30,000.  Check whether Mr. Bacchan is correct at 95% confidence level.  

 

He also claims that when CRIM = 0, the average price of the property will be 24.033. Is he correct? Explain your conclusion.

  

 

 

 

 

Q6. Tuck Maintenance:  

A trucking company wants to predict its yearly maintenance expense for its trucks using miles driven. Its data is saved in the file: MLR_TruckMaintenence.xlsx

a)  Estimate the MLR equation for maintenance expense vs miles driven.

b)  Interpret R-Squared for this dataset.

 

 

 

Q7. MLR – Overhead Cost

Benedrix, a machine tool company in interested in understand the impact of machine hours and production run, on its overhead cost.  

 

The data on a monthly basis for 3 years is provided in the dataset:

MLR_Q09_FactoryOverhead.csv

 

Fit the regression equations:  

•      Overhead = F (machine hours)

•      Overhead = F (production runs)

 

a)  Is production run strongly correlated with machine hours?

b)  Find the R-Squared in both the above cases?

c)   Which variable is a better predictor of Overhead cost?

 

 

The data files can be found here: https://github.com/Accelerate-AI/Data-ScienceGlobal-Bootcamp/tree/main/ClassAssignment/Assignment05