Class 10 Notes
  • Home
  • 10th Class Notes
    • Physics 10
    • Class 10 Notes
    • Pak Study 10th
    • CHEMISTRY 10 NOTES
    • Physics 10 Class
    • English Notes 10
    • Biology 10 Class
    • English Notes
    • Pak Study 10 Class
  • Articles
    • Education qoutes
    • DIT
  • English 4th Years
  • 9th Class Notes
    • Physics 9th
    • English 9th
    • Islamiat 9
  • Download file
  • Class 12 Notes
No Result
View All Result
  • Home
  • 10th Class Notes
    • Physics 10
    • Class 10 Notes
    • Pak Study 10th
    • CHEMISTRY 10 NOTES
    • Physics 10 Class
    • English Notes 10
    • Biology 10 Class
    • English Notes
    • Pak Study 10 Class
  • Articles
    • Education qoutes
    • DIT
  • English 4th Years
  • 9th Class Notes
    • Physics 9th
    • English 9th
    • Islamiat 9
  • Download file
  • Class 12 Notes
No Result
View All Result
Class 10 Notes
No Result
View All Result
Home Statistics Class 11

Statistics – Chapter 4 (Measure of Dispersion)

June 26, 2021
in Statistics Class 11
0
ADVERTISEMENT

Q.3) Explain the concept of regression and correlation, and describe the main properties of Karl-Pearson’s coefficient of correlation.

Table of Contents

    • Q.3) Explain the concept of regression and correlation, and describe the main properties of Karl-Pearson’s coefficient of correlation.
  • Statistics – Chapter 4 (Measure of Dispersion)
    • Q.4) What is a scatter diagram. Explain the meaning of regression of Y on X and X on Y.
    • Q.5) What is meant by least-squares method. Describe briefly the properties of the least-squares regression line.
    • Q.6) Differentiate between regression and correlation, giving examples.
    • Q.7) Explain with suitable examples the concept of correlation coefficient between two variables.

Answer:
Regression:

Regression is the relationship between one dependent and another independent variable (s). If there is only one independent variable, the regression is said to be simple or linear otherwise the regression is said to be multiple. For example, the yield of wheat depends upon the fertilizer, seeds, water, etc. In this example, the yield of wheat is the dependent variable, whit fertilizer; seeds and water are independent variables. The values of independent variables are assumed to be fixed, that is, it is not a random variable. On the other hand, the dependent variable, whose values are determined based on the independent variable, is a random variable.
Correlation:
Correlation is the interdependence between two or more variables. I correlation, it is assumed that all the variables are random variables. The correlation between two variables is said to be simple or linear, otherwise, the correlation is said to be multiple. Two variables are said to be correlated when an increase or decrease in one variable corresponds to an increase (decrease in the other variable. If either the variables increase or decrease the correlation will be positive and if they go in the opposite direction the correlation will be negative.

Statistics – Chapter 4 (Measure of Dispersion)

Read more: Statistics Chapter 2 (Collection and presentation of Data) | Class 11 Notes
Properties of Karl-Pearson correlation coefficient.

  • It is symmetrical with respect to variables. That is rxy = ryx
  • It is independent from the origin and scale. That is ruv =rvu
  • It is a number, which lies between ± 1.
  • It is the geometric mean of two regression coefficients.

Q.4) What is a scatter diagram. Explain the meaning of regression of Y on X and X on Y.

Answer:
To plot the bivariate data on the graph paper is called a scatter diagram with the help of scatter diagram the relationship between two variables studying. Values for the independent variable are shown on the horizontal axis and the corresponding values of the dependent variable are shown by vertical axis. The scatter diagram provides an over view of the data and enables us draw preliminary conclusion about a possible relationship between t variables.
Regression line of y on x: – this is a line, which may give the best possible mean values of y for given values of. It describes the variation in the values of y for a given variation in the values of x. In algebraic notation the equation of regression of y on x is Y= a+ b X.
Regression line of x on y: –
 this is a line, which may give the best possible mean values of “x” corresponding to variation in the values of “y”. i.e. X = a +b Y.

Q.5) What is meant by least-squares method. Describe briefly the properties of the least-squares regression line.

Answer:
The method of least square is an objective and efficient method of determining the best fitting curve. The least square method provides an estimated regression equation that minimizes the sum of squares deviations between the observed values of the dependent variable and the estimated values of the dependent variable. This method is used to find the straight line that provides the best approximation for the relationship between the independent and dependent variables.
PROPERTIES OF LEAST SQUARE REGRESSION LINE:
The sum of squares of the deviations from the regression line is minimum.
The regression line always passes through the points the means of the variables.
The sum of the deviations of the actual values from the regression line is always equal to zero. That is ∑(Y – Ŷ) = 0.

Q.6) Differentiate between regression and correlation, giving examples.

Answer:
Regression:
Regression is the relationship between one dependent and other independent variable (s). It provides an estimate to be used for estimating or predicting the average value of the dependent variable from the known values of the independent variable. In regression, the dependent variable is assumed a random variable whereas the independent variables are assumed to have fixed values, i.e.; they are chosen non-randomly. For example, the yield of wheat is depending upon the fertilizer etc.
Correlation:
Correlation is a measure of the degree to which any two variables vary together. For example, the length of an iron bar will increase as the temperature increase. The main difference in correlation and regression is that in correlation both the variables are random but in regression, one is random and the other non-random.

Q.7) Explain with suitable examples the concept of correlation coefficient between two variables.

Answer:
Correlation is measured by its coefficient “r” derived by Karl-Pearson. The value of “r” lies between ± 1. Where the magnitude of r indicates the strength of a linear relationship while its sign indicates the direction. If r = +1, it indicates perfect positive correlation. If r = -1, it indicates perfect negative correlation. If r = 0, it indicates no linear relationship or no correlation.

Read more: Statistics Class 11 Notes Cha 1 (Introduction To Statistics)

SendShare234Tweet146Pin53Send

Related Posts

DIT 2nd Semester 2012 to 2020 Previous Papers

Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution)

by admin
June 27, 2021
0

Hypergeometric and binomial Probability Distribution (Hypergeometric and binomial Probability Distribution) Chapter 8 Q.1 a). The telephone company reports that among 5000...

Homeostasis Biology Notes Class 10 Chapter No 11

Statistics Chapter 7 (RandomVariable and Probability Distribution)

by admin
June 27, 2021
0

Class 11 Notes for all pakistani boards Statistics Chapter 7 (RandomVariable and Probability Distribution). Statistics Chapter 7 (RandomVariable and Probability...

Happy September 6th

Statistics Chapter 6 (Probability) | Class 11 for KPK

by admin
June 27, 2021
0

Economics Notes for class 11 Chapter Number six Probability question and answer for all pakistani boards. Q.6.1) Define a set,...

Please login to join discussion

  • KPK Class 10th Maths Notes Pdf Download All Chapter
  • KPK Board Class 10th English Book Notes
  • Sslr V2 Login | SSLR Local Application
  • Unit 1 Handwritten Class 10 English Notes
  • English Notes Class 10 Unit 1 to Unit 15
  • Computer science Notes Pdf Download all chapters
  • Biology Class 10 Notes PDF Download for KPK | Unit 10 to Unit 18
  • unit 3 dreams handwritten class-10 english notes
  • Class 10 Notes | G10 all Subjects Notes
  • New Updated CLASS 10 ENGLISH HANDWRITTEN NOTES

Subscribe to Blog via Email

Enter your email address to subscribe to this blog and receive notifications of new posts by email.

Join 6 other subscribers

June 2022
M T W T F S S
 12345
6789101112
13141516171819
20212223242526
27282930  
« May    

Archives

  • Home
  • 10th Class Notes
  • Articles
  • English 4th Years
  • 9th Class Notes
  • Download file

© 2022 Class 10 Notes

No Result
View All Result
  • Home
  • 10th Class Notes
    • Physics 10
    • Class 10 Notes
    • Pak Study 10th
    • CHEMISTRY 10 NOTES
    • Physics 10 Class
    • English Notes 10
    • Biology 10 Class
    • English Notes
    • Pak Study 10 Class
  • Articles
    • Education qoutes
    • DIT
  • English 4th Years
  • 9th Class Notes
    • Physics 9th
    • English 9th
    • Islamiat 9
  • Download file

© 2022 Class 10 Notes