Regression Analysis: Correlation, Prediction, and Model Building

This assignment focuses on regression analysis, exploring the correlation between weight and various variables like height, leg length, arm length, arm circumference, and waist. The student calculates correlation coefficients, identifies potential misleading correlations, and builds a regression model to predict weight using height as the best predictor. The assignment includes the regression equation, assesses the significance of the slope, interprets the slope's meaning, and determines the coefficient of determination, explaining its implications. The solution also provides references to relevant statistical resources, including Draper & Smith (2014), Montgomery, Peck, & Vining (2012), and Seber & Lee (2012).

Running head: REGRESSION ANALYSIS 1
Regression Analysis
(Name of Student)
(Institutional Affiliation)
(Date of Submission)

REGRESSION ANALYSIS 2
Find the correlation for Weight with the following variables
Correlation with Weight
Height 0.7883
Leg Length 0.2718
Arm Length 0.8573
Arm Circumference 2.9706
Waist -0.9475
Based on the correlation coefficient, which of the variables would not be good predictors
of weight
Based on the correlation coefficients, leg length and Arm Circumference would not be a
good predictor of weight since they have absolute correlation coefficients of 0.2718 and
2.9706 as compared to other variables which are relatively approximates i.e. between (-1 and
+1)
Which of the correlation coefficients might be misleading? Justify your answer – attach all
relevant materials that support your position.
The correlations that might be misleading in this case are those of ‘Waist’ and ‘Leg Length’
which are -0.9475 and 0.2706 respectively.
These values suggest a stronger correlation between weight and the variables which are not
right according to scholars and other related researches. According to Wiley (2016) and other
related researches, the waist and leg length are founds the basis of body mass in human
beings and thus an individual with longer legs and broader weights will always have much
weight.

REGRESSION ANALYSIS 3
Build a regression model with the best predictor of weight. Write the regression equation
below
The best predictor of weight in this case is height
The regression equation obtained is;
Weight = 30.123 + 0.7883 (Height); where 30.123 is the constant term in this model and
0.7883 as the model slope.
Is the slope significant?
In this case, the slope is much significant because the value which is r = 0.7833 is relatively
more close to 1. Thus very significant value.
Interpret the slope
The slope is the regression model above is a positive one (r = 0.7883).
This implies that an increase in weight is due to an increase in height. Intuitively, this also
suggests that individual with increased heights have greater weights
What is the coefficient of determination for your model? Interpret the coefficient of the
determination.
The coefficient of the determination our case here is R squared = 0.62 (which is 62%). This is
basically the proportion of variance in the in the dependent variable which in this case is
weight. Hence this implies that a variability of 642% in weight can be explained by the
difference in the other variables.

REGRESSION ANALYSIS 4
References
Draper, N. R., & Smith, H. (2014). Applied regression analysis (Vol. 326). John Wiley &
Sons.
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to linear regression
analysis (Vol. 821). John Wiley & Sons.
Seber, G. A., & Lee, A. J. (2012). Linear regression analysis (Vol. 329). John Wiley & Sons.