Linear regression analysis of parent-child height data set

Catalog

brief introduction

“ If a father is tall, his son is tall , A short father makes a short son ”（ That is, the height of father and son is related , And is positively correlated ）、“ The mother is a nest high , The father is one higher ”（ That is, the height of the mother has a greater impact on the children than that of the father ） Whether the customs and legends of are established ？ Please be there. “ Height of parents and children ” Data sets （ Galton data set ） On the basis of this, we use linear regression to make scientific analysis .
1） Select the height data of father and son as X-Y, use Excel Calculate the linear regression equation and correlation coefficient 、 variance 、p It's worth waiting for , Judge whether the regression equation is tenable . Now if you have data for a new family , Father's height is known 75 Inch , Please measure the height of your son ？
2） Select the height data of mother and child as X-Y, use Excel Calculate the linear regression equation and correlation coefficient 、 variance 、p It's worth waiting for , Judge whether the regression equation is tenable .
3） Based on the above data , Clarify your analysis of whether the custom statement is correct .
4） You can use multiple linear regression , Calculate the father 、 The regression equation of the height of mother and son ？

One 、 Father and son height data

1、 regression analysis

Data analysis


Take father's height as X, The height of the child is Y

View analysis results

Set the starting value of coordinates

Add trendline

Display the analytical formula of fitting line

View results

The correlation coefficient ：-0.0374
variance ：0.51779
p value ：0.480549
Fitting equation ：y=-0.0374x+77.683

2、 Height prediction

problem ： Father's height is known 75 Inch , Measure the height of your son ;
y=75*(-0.0374)+77.683=74.878

From the forecast data , There is no positive correlation between father's height and children's height , The saying of custom is wrong . When my father is 75 when , According to the table, there are children whose height is lower than the predicted height .

Two 、 Height data of mother and child

1、 regression analysis

The steps are the same as above , Here is the analysis result directly .

Add trend line , Displays the fitted line equation

2、 related data

The correlation coefficient ：0.4134
variance ：4.69972
P value ：0.043075
Fitting equation ：y=0.4134*x+35.292

3、 Relevant numerical knowledge

The characteristics of relational numbers :
The correlation coefficient r Is a statistic that represents the strength and direction of linear correlation between two random variables , It's one A dimensionless number , Value range -1≤r≤1;r The positive and negative values of indicate the direction of linear correlation between two variables , namely r>0 It's positive correlation ,r<0 It's a negative correlation ,r=0 Zero correlation ; r And regression coefficient b The same symbol as ;. r The absolute value of indicates the closeness of the linear correlation between the two variables ,|r | The more close to 1, Indicates that the higher the closeness ,|rI The more close to 0, Indicates that the lower the closeness .

Variance analysis and regression analysis are related but not identical analysis methods . Analysis of variance mainly studies the qualitative relationship between the influence of each variable on the results , So as to eliminate the variables that have little impact on the results , Improve the efficiency and accuracy of the test . Regression analysis is to study the quantitative relationship between variables and results , Get the corresponding mathematical model . In regression analysis , It is necessary to conduct variance analysis on the impact of each variable on the results , To eliminate the variables that have little influence , Improve the effectiveness of regression analysis .
In regression analysis , Analysis of variance will be used to judge the impact of each variable on the results , So as to determine which factors should be included in the regression equation , Which should not be included in the regression equation due to the small variance of the results .
If P Great value , Illustrate this T The value is very close to the origin , and P Small values , It means T The value is far from the origin （T The greater the absolute value of ,P The smaller it is ）, Based on the above analysis ,P The smaller the better. .

3、 ... and 、 Summary and references

1、 summary

A thorough understanding of linear regression analysis .

2、 Reference material

Excel Do linear regression analysis .
How to judge whether the regression equation is tenable .