Question

In: Statistics and Probability

Each of the following statements contains an error. Describe each error and explain why the statement...

Each of the following statements contains an error. Describe each error and explain why the statement is wrong.

(a) If the residuals are all negative, this implies that there is a negative relationship between the response variable and the explanatory variable.

(b) A strong negative relationship does not imply that there is an association between the explanatory variable and the response variable.

(c) A lurking variable is always something that can be measured.

Solutions

Expert Solution

(a)- The error in the statement is given as follows:-

The difference between the original value and the predicted value is known as a residual. When residual is positive ,this indicates that the predicted value is less than the original data value of the response variable.

hence wrong in the statement is that a positive residual does not imply that the relation between the response and explanatory variable is positive. but the true statement is

If the residuals are all positive, this implies that the predicted value of the response variable is smaller than the original data value

(b)- Negative relationship between two variables describes such a way that if one variable increases then other decreases

hence A strong negative relationship imply that there is a negative association between the explanatory variable and the response variable.

(c)- The error in the statement "lurking variable is always a response variable' is explained below:

lurking variable is different from response and explanatory variable in the experiment. This effects the relation between the response and explanatory variable in the experiment. This variable cannot be controlled during experiment.

hence The wrong in the statement is that lurking variable can not be always measured.

please like ?

orchestra answered 1 year ago
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