A researcher conducted a survey among all the male employees in Research Square Park (just like Research Triangle Park). Among other questions, she asked a randomly selected set of male employees in the past three months (1) how much they have spent on skin-care products and (2) how much tennis they have watched on TV. After collecting the data, she performed a simple linear regression analysis. She was interested in the relationship between the time spent on watching tennis and the money spent on skincare. She treated the number of hours in the past three months watching tennis as the independent variable, and she treated the amount spent on skin-care products in the past three months as the dependent variable. She used StatCrunch to get the following output: Austin, a male employee in RSP, spent 10 hours watching tennis and 200 on skin-care products during the past three months. What is the corresponding residual value?

Question

06-03-2024
Mathematics

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A researcher conducted a survey among all the male employees in Research Square Park (just like Research Triangle Park). Among other questions, she asked a randomly selected set of male employees in the past three months (1) how much they have spent on skin-care products and (2) how much tennis they have watched on TV. After collecting the data, she performed a simple linear regression analysis. She was interested in the relationship between the time spent on watching tennis and the money spent on skincare. She treated the number of hours in the past three months watching tennis as the independent variable, and she treated the amount spent on skin-care products in the past three months as the dependent variable. She used StatCrunch to get the following output: Austin, a male employee in RSP, spent 10 hours watching tennis and 200 on skin-care products during the past three months. What is the corresponding residual value?

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ayameygarcia39 ayameygarcia39 · Answer 1 · 2024-03-06T01:13:57+01:00

To find the corresponding residual value for Austin, the researcher would first calculate the predicted value of the amount spent on skincare products based on the regression equation obtained from the analysis. Then, the residual value can be found by subtracting the predicted value from the actual value.

Since the output from StatCrunch was not provided, I can't give you the exact predicted value. However, assuming the regression equation obtained from the analysis is of the form:

\[ \text{Amount spent on skincare products} = \beta_0 + \beta_1 \times \text{Hours spent watching tennis} + \varepsilon \]

You would plug in Austin's data:

\[ \text{Amount spent on skincare products} = \beta_0 + \beta_1 \times 10 \]

Then, you would compare this predicted value with the actual amount Austin spent on skincare products (which is 200). The residual value is the difference between the actual and predicted values.

So, if the predicted amount of money Austin spent on skincare products based on the regression equation is, for example, 180, then the corresponding residual value would be \( 200 - 180 = 20 \).