Consider the following two matrices
A =

B =  

(i) Find the rank of 'A' and 'B'

(ii) Show that (AB)⁻¹ = B⁻¹ A⁻¹

(iii) Show that (A⁻¹)⁻¹ = A

(iv) Show that (B⁻¹)⁻¹ = B

Fit a simple linear regression model on the data given in Question 2 for non-smokers only and obtain the followings:

(i) Diagonal of the hat matrix. Also, check the leverage points, if any.

(ii) Cook's Distances. Also, verify the influence points, if any.

A logistics company wants to predict the delivery efficiency score of its drivers based on two primary factors: years of driving experience and average hours of sleep per night. The data for 10 drivers are recorded as follows:

Based on the image provided, here is the data transcribed into a table format:

To investigate the effect of Age (in years) and Smoking Status (Group 1: Non-Smokers, Group 2: Smokers) on Systolic Blood Pressure (in mmHg), the following data were collected:

The txt from the table in the image is provided below:

(i) Fit a multiple regression model.

(ii) Obtain the individual regression models for Non-Smokers and Smokers separately based on the main model.

(iii) Test the significance of the overall fitted regression model at the 5% level of significance.

To investigate the effect of Age (in years) and Smoking Status (Group 1: Non-Smokers, Group 2: Smokers) on Systolic Blood Pressure (in mmHg), the following data were collected:

State whether the following statements are true or false and also give the reason in support of your answer.

(i) The model Y = BX + & is a linear model.

(ii) If total and residual sum of squares for a dataset are 124 and 15.5, respectively, then the coefficient of determination is 0.875.

(iii) We use Cook's distances to identify the autocorrelation of the error terms.

(iv) If the coefficient of determination for the auxiliary regression model of the explanatory variable X₁ is 0.8, the VIF for X₁ will be 5.

(v) We use baseline category logit models when we have ordered categories of a response variable.

Write a Python program using NumPy to
(i) Create following two matrices P and Q with following elements.
$
(ii) Compute the (a) Addition, (b) Multiplication, (c) Determinant and (d) Inverse of these matrices.
(iii) Combine the given matrices row-wise and determine the transpose of the combined matrix.
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What are different ways to create a NumPy array? Explain any two with examples.

Describe any two Python libraries used for data visualization.

Describe the while loop with an example program.

 Explain how file handling works in Python for text files. Mention different file modes, and a short description of read(), readline() and write().

Describe the key features of Spyder.

Write a Python program to accept a list of tuples (product_name, price) for 5 items from the user, then sort the list by price in descending order using a function.

Find and correct the error in the following code.

import numpy as np

arr = np.array[4, 5, 6]

print(arr)

Write the output of the following Python code.

nums = [10, 20, 30, 40, 50]

print(nums[-2])

एक खुदरा (रिटेल) कंपनी के विभिन्न विभागों में डेटा के इस्तेमाल का उल्लेख कीजिए। 9. नियंत्रण (Controlling) की विभिन्न विशेषताएँ क्या हैं? नियंत्रण प्रबंधन के अन्य कार्यों से किस प्रकार भिन्न है?

खुदरा (रिटेल) अंतः क्रियाओं में संचार के विनिमय सिद्धांत (Exchange Theory of Communication) को कैसे लागू किया जाता है? 

प्रौद्योगिकी-सक्षम संचार (Technology Enabled Communication) के सकारात्मक और नकारात्मक प्रभावों पर चर्चा कीजिए।

ग्राहक संचार प्रबंधन (Customer Communication Management) खुदरा विक्रेता की ब्रांडिंग को कैसे बेहतर बनाने में मदद कर सकता है? 

स्वेच्छाचारी (Autocratic), लोकतांत्रिक (Democratic) और अहस्तक्षेपकारी / लैसेज़-फेयर (Laissez Faire) नेतृत्व शैलियों में अंतर स्पष्ट कीजिए।

सीमांत विश्लेषण (Marginal Analysis) और लागत-लाभ विश्लेषण (Cost-Benefit Analysis) विकल्पों के मूल्यांकन के उपकरण के रूप में कैसे कार्य करते हैं?