STA404 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || REGRESSION AND CORRELATION ANALYSIS || BY VuTech

STA404 ASSIGNMENT NO. 1 FALL 2022

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STA404 ASSIGNMENT NO. 1 FALL 2022 || 100% RIGHT SOLUTION || REGRESSION AND CORRELATION ANALYSIS || BY VuTech

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Assignment No.1 (Course STAT404)

 Fall 2022 (Total Marks 15)

Deadline

Your Assignment must be uploaded/ submitted before or on

13^th  December ,  2022, Time 23:59

(STUDENTS ARE STRICTLY DIRECTED TO SUBMIT THEIR ASSIGNMENT BEFORE OR BY DUE DATE. NO ASSIGNMNENT AFTER DUE DATE WILL BE ACCEPTED VIA E.MAIL).

Rules for Marking

It should be clear that your Assignment will not get any credit IF:

·      The Assignment submitted, via email, after due date.

·      The submitted Assignment is not found as MS Word document file.

·      There will be unnecessary, extra or irrelevant material.

·     The Statistical notations/symbols are not well-written i.e., without using MathType software.

·      The Assignment will be copied from handouts, internet or from any other student’s file. Copied material (from handouts, any book or by any website) will be awarded ZERO MARKS. It is PLAGIARISM and an Academic Crime.

·      The medium of the course is English. Assignment in Urdu or Roman languages will not be accepted.

·      Assignment means Comprehensive yet precise accurate details about the given topic quoting different sources (books/articles/websites etc.). Do not rely only on handouts. You can take data/information from different authentic sources (like books, magazines, website etc.) BUT express/organize all the collected material in YOUR OWN WORDS. Only then you will get good marks.

Objective(s) of this Assignment:

 

The assignment is being uploaded to build up the concepts of Correlation Coefficient and Square of Residuals.

 

 

 

 

 

 

Question # 1

 

The data below gives the marks obtained by 10 pupils taking Maths and Physics tests

 

Pupil	A	B	C	D	E	F	G	H	I	J
Maths Marks  (out of 30)    x	20	23	8	29	14	11	11	20	14	14
Physics Marks  (out of 30)   y	30	35	21	33	33	26	22	31	33	36

 

Calculate the coefficient of correlation.

 

Solution:

Pupil	Maths Marks  (out of 30)    X	Physics Marks  (out of 30)   Y	XY	`X^2`	`Y^2`
A	20	30	600	400	900
B	23	35	805	529	1225
C	8	21	168	64	441
D	29	33	899	841	1089
E	14	33	462	196	1089
F	11	26	286	121	676
G	11	22	242	121	484
H	20	31	620	400	961
I	14	33	462	196	1089
J	14	36	504	196	1296
∑	146	300	5048	3064	9250

Here n = 10

`r = \frac{n \times (\sum (XY ) - (\sum X \times \sum Y))}{\sqrt {(n \times \sum X^2 - \sum ( X )^2) \times (n \times \sum Y^2 - \sum ( Y )^2)}}`

`r = \frac{10 \times (5048 - (146 \times 300))}{\sqrt {(10 \times 3064 - \sum (146)^2) \times (10 \times 9250 - \sum ( 300)^2 ) }}`

`r = \frac{10 \times (5048 - 43800)}{\sqrt {(30640 - 21316) \times (92500 - 90000)}}`

`r = \frac{10 \times  - 38752}{\sqrt {9324 \times 2500}}`

 `r = \frac{ - 387520}{\sqrt {23310000}}`

 `r = \frac{- 387520}{4828.0431}`

`r =  - 80.2644`

 

Question # 2

 

By using the regression line `\hat y = 0.7 + 2.9x` and the below data, find the squares-of-residuals.

 

x	y
-1	0
0	2
1	4
2	5

Solution:

 

x	y	`\hat y = 0.7 + 2.9x`	Error `( y - \hat y)`	Squared Error `( y - \hat y)^2`
-1	0	-2.2	2.2	4.84
0	2	0.7	1.3	1.69
1	4	3.6	0.4	0.16
2	5	6.5	-1.5	2.25
∑				8.94

 

 

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