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.

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