(2) A friend tells you that you should never be a patient in a teaching hospital
ID: 1168519 • Letter: #
Question
(2) A friend tells you that you should never be a patient in a teaching hospital because thedeath rate among patients in teaching hospitals is higher than in other hospitals.(b) Write down a regression equation where the dependent variable is the death rate in ahospital, and one explanatory variable is whether a hospital is teaching or not.(c) Interpret the meaning of the regression coefficient on the explanatory variable.(d) What sign of the coefficient in (c) would correspond to your friend’s story? (e) Do you agree with the interpretation of the coefficient your friend provides? If not,explain why not?(f) How can you change the regression equation to support your explanation in (e)?
Explanation / Answer
b)The formula for a regression line is. Y' = bX + A. where Y' is the predicted score, b is the slope of the line, and A is the Y intercept
c)when the regression line is linear (y = ax + b) the regression coefficient is the constant (a) that gives the rate of change of one variable (y) as a function of changes in the other (x); it is actually slope of the regression line
d)a negative sign
e)
1.Not taking confidence intervals for coefficients into account.
Even in case a regression coefficient is (correctly) interpreted as a rate of change of a conditional mean (rather than a rate of change of the response variable), it is essential to take into account the uncertainty in the estimation of the regression coefficient.
2. Interpreting a coefficient that is'nt statistically significant.
Interpretations of outcomes that are not statistically significant are made quite often. If the t-test for a regression coefficient is not statistically significant, it may not be correct to interpret the coefficient. A better alternative could be to state, "No statistically significant linear dependence of the mean of Y on x was seen.
f)it isn’t always straightforward to select the appropriate regression equation, more so when one is dealing with real life data. Sometimes we are faced with “noisy” data that doesn’t seem to quite fit any equation If most of the data looks like it follows a pattern, you could omit the outliers. Rather, if you ignore outliers, the data seems like it may be modeled by an exponential equation.
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