You have the following standardised regression model equation for a sample of data: ZŶi = 0.6ZXi

Variable Y is “Daily Amount of Water Consumed” (in litres)

Variable X is “Temperature” (in °C)

Which of the following statements is true based on the standardised regression equation?

Question

You have the following standardised regression model equation for a sample of data: ZŶi = 0.6ZXi

Variable Y is “Daily Amount of Water Consumed” (in litres)

Variable X is “Temperature” (in °C)

Which of the following statements is true based on the standardised regression equation?

BlackTom AI · Accepted Answer

The question presents a standardized regression model: ZŶi = 0.6 ZXi, where ZŶi is the standardized value of Y (Daily Amount of Water Consumed in litres) and ZXi is the standardized value of X (Temperature in °C).

First, recall what a standardized regression coefficient represents. When both the dependent and independent variables are standardized (converted to z-scores with mean 0 and standard deviation 1), the slope coefficient in the regression equation indicates how many standard deviation units the dependent variable changes for a one standard deviation unit change in the independent variable.

Option analysis:
- Option: 'If Temperature increased by 1 standard deviation unit, we would expect the Daily Amount of Water Consumed to increase by 0.6 standard deviation units.'
  This statement directly reflects the meaning of the standardized slope of 0.6. A one-unit change in ZXi (i.e., a 1 SD increase in Temperature) is associated with a 0.6-unit change in ZŶi (i.e., a 0.6 SD increase in Daily Water Consumption). In standardized terms, the coefficient 0.6 is the expected change in the standardized Y for each 1 standard deviation change in the standardized X.

Since the model is in standardized form, there isn’t any additional scaling or transformation to consider beyond this interpretation. The coefficient does not refer to raw units (litres or degrees Celsius) but to standard deviation units, which is the whole point of standardization.

Potential misconceptions to avoid:
- Thinking the coefficient applies to raw units (e.g., litres per degree) is incorrect because the variables are standardized, not in their original scales.
- Believing the coefficient would imply a decrease or no effect would ignore the positive 0.6 value shown in the model.

In summary, the given statement correctly interprets the standardized regression coefficient: a 1 SD increase in Temperature is associated with a 0.6 SD increase in Daily Water Consumption, according to the model.

类似问题

You have a sample of 20 individuals, and run a simple regression analysis using statistical software (with dependent variable Y, and independent variable X). One of the output tables is as follows: What is the standardised regression equation (to two decimal places)?

Refer to Scenario 8-1. You can see from the information in (1) that Charlie got a lot more education than the average person. When compared to the average person, the standardized regression model predicts that

In a regression equation applied to data in which the X and Y scores are standardized (i.e., transformed into z scores), what value of zY would you predict for a zX value of 0?

In a regression equation applied to data in which the X and Y variables are both standardized (i.e., transformed into z scores), what is the value of the intercept?

When evaluating a new project, firms should include in the projected cash flows all of the following EXCEPT:

Provide the best rationale for what's wrong with supply chains today?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单