1 of 8 0-day streak

Calculate and interpret the coefficient of determination

Question 1 of 8

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The observed variables are floor area (m²) (explanatory) and quarterly electricity use (kWh) (response). Their reported linear correlation is r = 0.36

Interpret explained variation for a simple least-squares linear model with an intercept. It is a proportion of observed response variation relative to the mean-only baseline, not a causal effect or a percentage of cases

(a)1 mark

Calculate r². Give the decimal to 3 decimal places

r² Format: 3 d.p.

(b)1 mark

What does r² = 0.130 mean for these paired observations?

The value 0.360 is r rather than r², so it gives the percentage of variation explained in quarterly electricity use (kWh)

The coefficient indicates that 13% of the variation in quarterly electricity use (kWh) is explained by variation in floor area (m²)

13% of the variation in floor area (m²) is explained by variation in quarterly electricity use (kWh)

Keep the sign of r in the coefficient, so use 0.360; its sign gives the direction of the association