Regression Model Linear Models

Question: Describe about the Regression Model for Linear Models. Answer: (LR-1) Purpose: To estimate the blood fat content based on age using a linear model Data: the data on Age and blood fat content is retrieved S/No. Age (Years) Fat content S/No. Age (Years) Fat content 1 46 354 14 23 254 2 20 190 15 60 395 3 52 405 16 48 434 4 30 263 17 34 220 5 57 451 18 51 374 6 25 302 19 50 308 7 28 288 20 34 220 8 36 385 21 46 311 9 57 402 22 23 181 10 44 365 23 37 274 11 24 209 24 40 303 12 31 290 25 30 244 13 52 346 (LR-2) Scatterplot: As one would expect, as the age increases so should the blood fat content. This gives a somewhat linear trend. (LR-3) Line of Best Fit (Regression Line) y = 5.3207x + 102.58 where x = Age (Years) and y = blood fat content (LR-4): The slope is 5.3207 and is positive since the blood fat content increases with age. The slope indicates that in general, the blood fat content increase by 5.3207 with a one year increase in age, and so the blood fat content increases at an average rate of 1(5.3207) = 5.3207 for a unit increase in age. (LR-5): Values of r2 and r: r2=0.7012 We know that the slope of the regression line is positive so the correlation coefficient r must be positive. Recall that r = +1 corresponds to perfect positive correlation, and so r = 0.8374 indicates moderately strong positive correlation (relatively close to +1 but not very strong). (LR-6) Prediction: For someone age 50, substitute x = 50 to get y = 5.3207(50) + 102.58 368.615. The regression line predicts a blood fat content of 368.615 for a person aged 50 years old. (LR-7) Narrative: The data consisted of the blood fat content and the ages of 25 individuals. The data exhibit a moderately strong upward linear trend. The regression line predicts a blood fat content of 368.615 for an individual aged 50 years old. Will the regression line's prediction be the same (Upward linear trend) if we use weight as the independent variable? Using the weight (Kilograms) as the independent variable and Blood fat content as the dependent variable, our regression line is y = 1.6223x + 199.3. When x = 80, the prediction is y = 1.6223(80) + 199.3 329.084. Its important to note that r2 = 0.0704 and for the positively sloping line, the correlation coefficientis , not as strong as when we considered the age (years) as the independent variable. Conclusion: In this paper, I have examined two linear models, using different independent variables and both have positive correlation coefficients though the strengths of correlation differ. One model uses age (years) as the independent variable while the other uses weight (Kilograms) as the independent variable.