ScienceMathH4.4
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H4.4

Waylen Murphy avatar Waylen Murphy
8 September 2022
4.7 (114 reviews)
11 test answers

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question
For what types of associations are regression models​ useful?
answer
Regression models are useful only for linear associations. If the association is not​ linear, a regression model can be misleading and deceiving.
question
What type of effect can outliers have on a regression​ line?
answer
A regression line is a line of​ means, and outliers have a big effect on the regression line.
question
When one has influential points in their​ data, how should regression and correlation be​ done?
answer
When one has influential points in their​ data, they should do the regression and correlation with and without these points and comment on the differences.
question
Since outliers can greatly affect the regression line they are also called​ _______ points.
answer
Since outliers can greatly affect the regression​ line, these types of observations are called influential points because their presence or absence has a big effect on conclusions.
question
Attempting to use the regression equation to make predictions beyond the range of the data is called​ _______.
answer
Extrapolation means that one uses the regression line to make predictions beyond the range of the data. This practice can be​ dangerous, because although the association may have a linear shape for the range one is​ observing, that might not be true over a larger range.
question
Under what conditions can extrapolation be used to make predictions beyond the range of the​ data?
answer
Extrapolation can never be used to make predictions beyond the range of the data.
question
The value that measures how much variation in the response variable is explained by the explanatory variable is called the​ _______.
answer
The coefficient of determination is the correlation coefficient​ squared; r2. In​ fact, this statistic is often called​ r-squared. This value measures how much variation in the response variable is explained by the explanatory variable.
question
A.What is an influential​ point? b. It has been noted that people who go to church frequently tend to have lower blood pressure than people who​ don't go to church. Does this mean you can lower your blood pressure by going to​ church? Why or why​ not? Explain.
answer
An influential point is a point that changes the regression equation by a large amount. When there are influential points in the​ data, it is good practice to try the regression and correlation with and without these points and to comment on the difference. Correlation does not imply causation. Going to church may not cause lower blood pressure. Just because two variables are related does not show that one caused the other. It could be that healthy people are more likely to go to​ church, or there could be other confounding factors.
question
a. What is extrapolation and why is it a bad idea in regression​ analysis? b. How is the coefficient of determination related to the​ correlation, and what does the coefficient of determination​ show? c. When testing the IQ of a group of adults​ (aged 25 to​ 50), an investigator noticed that the correlation between IQ and age was negative. Does this show that IQ goes down as we get​ older? Why or why​ not? Explain.
answer
is prediction far outside the range of the data. These predictions may be incorrect if the linear trend does not​ continue, and so extrapolation generally should not be trusted. The coefficient of determination is the square of the​ correlation, and it shows the proportion of the variation in the response variable that is explained by the explanatory variable. No, correlation does not mean causation.
question
If the correlation between height and weight of a large group of people is 0.71​, find the coefficient of determination​ (as a​ percent) and explain what it means. Assume that height is the predictor and weight is the​ response, and assume that the association between height and weight is linear.
answer
The coefficient of determination is 50.41​%. ​Therefore, 50.41​% of the variation in weight can be explained by the regression line.
question
Suppose a doctor telephones those patients who are in the highest​ 10% with regard to their recently recorded blood pressure and asks them to return for a clinical review. When she retakes their blood​ pressures, will those new blood​ pressures, as a group​ (that is, on​ average), tend to be higher​ than, lower​ than, or the same as the earlier blood​ pressures, and​ why?
answer
The new blood pressures will tend to be lower. Part of the high reading might be due to​ chance, and regression toward the mean predicts that a repeated measurement will be closer to the typical value.