Figure 2.
To check data relationship using plot(women)
Figure 3.
Summary statistic
Figure 4.
Model regression summary
Figure 5.
Testing the model with given weight values
Insight
The average height is 65.0, and weight is 136.7; the linear regression equation provided is of the form y = mx + b, where y (weight) represents the dependent variable and x (height) represents
the independent variable, m represents the slope, and b represents the intercept. Based on the equation, we can interpret the intercept as -87.52. This means that when height equals 0, the dependent variable is predicted to be -87.52. However, this interpretation may not be meaningful.
The equation can be represented as y= -87.52 + (3.45*height).
If the dependent variable and independent variable have a positive relationship in a linear regression, it is not possible to have a negative intercept. A negative intercept is only possible when the relationship between the dependent variable and the independent variable is negative.
In a positive relationship, as the independent variable increases, the dependent variable also increases. The intercept in this case represents the value of the dependent variable when the independent variable is zero. If the relationship is positive, the intercept will be positive as well, since the dependent variable will have a positive value even when the independent variable is zero.
An application or example of a positive relationship in linear regression could be predicting the weight of a person based on their height. In this case, the height would be the independent variable, and the weight would be the dependent variable. The relationship between height and weight is typically positive, meaning that as the height increases, the weight also increases. The intercept would represent the weight of a person when their height is zero, which is not meaningful in this context. Therefore, it is common to center the independent variable (subtract the mean from each data point) so that the intercept represents the weight of a person of average height. In this case, the intercept will be positive and will represent the average weight of a person of average height.
Depending on the context of the data and the dependent variable; for example, there is no negative height when referring to humans.
With positive residual means the predicted value is high
The model explains that, given the same data point of height as Figure 1, the values of the weight will be explained by the model as given in Figure 5.
Figure 6.
To standardize women data in R-studio for linear regression, you can use the scale() function. The scale() function centers and scales the data, which means it subtracts the mean of each variable from each observation and divides it by the standard deviation of that variable. This process ensures that each variable has a mean of zero and a standard deviation of one.
