please help!!
i have obtained the equation of the regression line for a previous question which is: y=62.4+0.663x
i had to use this to calculate the residual of a patient whose blood level was 142mg two days after a heart attack and was 116 four days after a heart attack. the explanatory variable was the patients blood level two days after a heart attack. i need to now explain why using my equation would be inappropriate to estimate the patients blood level four days after a heart attack when their blood level is 375mg two days after having a heart attack.
any ideas because im really stuck on this question thank you very much
The regression line was obtained under differing baselines. It is not applicable under changed conditions.
To understand why using the equation y = 62.4 + 0.663x would be inappropriate to estimate the patient's blood level four days after a heart attack when their blood level is 375mg two days after having a heart attack, we need to consider the limitations of the regression line and the changes in the explanatory variable.
The regression line is obtained by analyzing the relationship between two variables, in this case, the patient's blood level (y) and the time since the heart attack (x). The equation y = 62.4 + 0.663x represents the expected relationship between these variables based on the data used to create the regression line. However, it is important to note that this equation is only accurate within the range of the data used to create the regression line.
In this case, the regression line was derived from data where the patient's blood levels were 142mg two days after a heart attack and 116mg four days after a heart attack. The explanatory variable, which is the patient's blood level two days after a heart attack, was used to estimate their blood level four days after a heart attack.
The equation y = 62.4 + 0.663x assumes a linear relationship between the explanatory variable and the response variable. However, using this equation to estimate the patient's blood level four days after a heart attack when their blood level is 375mg two days after having a heart attack would involve extrapolation, which means extending the regression line beyond the range of the observed data.
Extrapolation is generally considered less reliable because it assumes that the relationship between the variables remains constant outside the observed range. In reality, this may not be the case, and the relationship between the variables may change under different conditions or for extreme values. Therefore, using the regression equation to estimate the patient's blood level four days after a heart attack with a blood level of 375mg two days after having a heart attack would not be appropriate and may lead to inaccurate results.
To estimate the patient's blood level accurately four days after a heart attack with a blood level of 375mg two days after having a heart attack, it would be best to collect additional data within that specific range or use alternative statistical methods specifically designed for extrapolation.