CODEWITHSUNDEEP
rregressionlinear-regressionlm
J_Throat
J_Throat

Reputation: 77

How to export regression equations for grouped data?

I have a data frame PlotData_df with 3 columns: Velocity (numeric), Height(numeric), Gender(categorical).

        Velocity Height Gender
1       4.1    3.0   Male
2       3.1    4.0 Female
3       3.9    2.4 Female
4       4.6    2.8   Male
5       4.1    3.3 Female
6       3.1    3.2 Female
7       3.7    3.0   Male
8       3.6    2.4   Male
9       3.2    2.7 Female
10      4.2    2.5   Male

I used the following to give regression equation for complete data:

c <- lm(Height ~ Velocity, data = PlotData_df)

summary(c)
#             Estimate Std. Error t value Pr(>|t|)   
# (Intercept)   4.1283     1.0822   3.815  0.00513 **
# Velocity     -0.3240     0.2854  -1.135  0.28915   
# Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# Residual standard error: 0.4389 on 8 degrees of freedom
# Multiple R-squared:  0.1387,  Adjusted R-squared:  0.03108 
# F-statistic: 1.289 on 1 and 8 DF,  p-value: 0.2892

a <- signif(coef(c)[1], digits = 2)
b <- signif(coef(c)[2], digits = 2)
Regression <- paste0("Velocity = ",b," * Height + ",a)
print(Regression)
# [1] "Velocity = -0.32 * Height + 4.13"

How can I extend this to display two regression equations (depending on whether Gender is Male or Female)?

Upvotes: 1

Views: 323

Answers (1)

Zheyuan Li
Zheyuan Li

Reputation: 73265

How can I extend this to display two regression equations (depending on whether Gender is Male or Female)?

You need a linear model with interaction between Height and Gender first. Try:

fit <- lm(formula = Velocity ~ Height * Gender, data = PlotData_df)

Then if you want to display fitted regression function / equation. You should use two equations, one for Male, one for Female. There is really no other way, because we decide to plug in coefficients / numbers. The following shows you how to get them.

## formatted coefficients
beta <- signif(fit$coef, digits = 2)
# (Intercept)  Height  GenderMale  Height:GenderMale
#        4.42   -0.30       -1.01               0.54 

## equation for Female:
eqn.female <- paste0("Velocity = ", beta[2], " * Height + ", beta[1])
# [1] "Velocity = -0.30 * Height + 4.42"

## equation for Male:
eqn.male <- paste0("Velocity = ", beta[2] + beta[4], " * Height + ", beta[1] + beta[3])
# [1] "Velocity = 0.24 * Height + 3.41"

If you are unclear why

  • the intercept for group Male is beta[1] + beta[3];
  • the slope for Male is beta[2] + beta[4],

you need to read around ANOVA and contrast treatment for factor variables. This question on Cross Validated: How to interpret dummy and ratio variable interactions in R has a very similar setting to yours. I made a very brief answer there on the interpretation of coefficients, so maybe you could have a look.

Upvotes: 1

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