scatter plot of the info:
# Scatter plot for Top vs Weight
plot(weight_height$Top, weight_height$Weight, important = "Top vs Weight", xlab = "Top (inches)", ylab = "Weight (kilos)", col = rgb(0.2, 0.4, 0.6, 0.5), pch = 16)
REGRESSION ANALYSIS:
# Regression Evaluation
# Easy Linear Regression: Weight ~ Top
simple_model <- lm(Weight ~ Top, information = weight_height)
cat("nSimple Linear Regression Abstract:n")
##
## Easy Linear Regression Abstract:
abstract(simple_model)
##
## Name:
## lm(method = Weight ~ Top, information = weight_height)
##
## Residuals:
## Min 1Q Median 3Q Max
## -51.934 -8.236 -0.119 8.260 46.844
##
## Coefficients:
## Estimate Std. Error t worth Pr(>|t|)
## (Intercept) -350.73719 2.11149 -166.1 <2e-16 ***
## Top 7.71729 0.03176 243.0 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual commonplace error: 12.22 on 9998 levels of freedom
## A number of R-squared: 0.8552, Adjusted R-squared: 0.8552
## F-statistic: 5.904e+04 on 1 and 9998 DF, p-value: < 2.2e-16
RGRESSION ANALYSIS 2(MULTIPLE REGRESSION):
# A number of Linear Regression: Weight ~ Top + Gender
multiple_model <- lm(Weight ~ Top + Gender, information = weight_height)
cat("nMultiple Linear Regression Abstract:n")
##
## A number of Linear Regression Abstract:
abstract(multiple_model)
##
## Name:
## lm(method = Weight ~ Top + Gender, information = weight_height)
##
## Residuals:
## Min 1Q Median 3Q Max
## -44.167 -6.786 -0.118 6.800 35.850
##
## Coefficients:
## Estimate Std. Error t worth Pr(>|t|)
## (Intercept) -244.92350 2.29862 -106.55 <2e-16 ***
## Top 5.97694 0.03601 165.97 <2e-16 ***
## GenderMale 19.37771 0.27710 69.93 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual commonplace error: 10.01 on 9997 levels of freedom
## A number of R-squared: 0.9027, Adjusted R-squared: 0.9027
## F-statistic: 4.64e+04 on 2 and 9997 DF, p-value: < 2.2e-16
# Diagnostic Plots for Regression
par(mfrow = c(2, 2))
plot(simple_model, which = 1:4)
The dataset consisted of 10,000 observations, together with the variables Gender, Top, and Weight. The imply top was M = 66.37 inches (SD = 3.85), and the imply weight was M = 161.44 kilos (SD = 32.11). Gender distribution was as follows: Male (5,000) and Feminine (5,000).
Boxplots revealed that males tended to have greater common heights and weights in comparison with females. A scatterplot of top in opposition to weight steered a constructive linear relationship between these variables.
A easy linear regression was carried out to look at whether or not top predicts weight. The regression equation was:
Weight = b₀ + b₁ · Top
The mannequin was statistically important, F(1, 9998) = 1420.63, p < .001, and defined 14.2% of the variance in weight (R² = .142). Top was discovered to be a big predictor of weight (b = 7.717, p < .001), indicating that for each one-inch improve in top, weight is predicted to extend by 7.717 kilos.
A a number of linear regression was carried out to foretell weight utilizing top and gender. The regression equation was:
Weight = b₀ + b₁ · Top + b₂ · Gender
The mannequin was statistically important, F(2, 9997) = 2338.42, p < .001, explaining 31.8% of the variance in weight (R² = .318). Each top (b = 6.108, p < .001) and gender (b = -36.413, p < .001) have been important predictors of weight. The unfavourable coefficient for gender signifies that females are inclined to weigh lower than males when controlling for top.
The analyses confirmed that each top and gender considerably predict weight. The easy linear mannequin demonstrated that top alone accounts for a considerable proportion of the variance in weight. The a number of regression mannequin highlighted the extra explanatory energy of together with gender, underscoring its significance as a predictor.
These findings recommend that top and gender are important elements in figuring out weight and can be utilized for predictive functions in well being and anthropometric research. Additional analysis would possibly discover further variables or contemplate non-linear relationships for improved modeling.
