DA0-002 Data Analysis Practice Question
Exhibit
Refer to the exhibit.
Call:
lm(formula = price ~ sqft_living + bedrooms + bathrooms, data = housing)
Residuals:
Min 1Q Median 3Q Max
-1.2345 -0.3456 -0.0123 0.3456 2.3456
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.123456 0.012345 10.000 <2e-16 ***
sqft_living 0.001234 0.000123 10.000 <2e-16 ***
bedrooms -0.056789 0.012345 -4.600 4.23e-06 ***
bathrooms 0.234567 0.045678 5.135 3.45e-07 ***
--
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.4567 on 496 degrees of freedom
Multiple R-squared: 0.789, Adjusted R-squared: 0.787
F-statistic: 617.8 on 3 and 496 DF, p-value: < 2.2e-16Given the linear regression output, which independent variable has the strongest effect on price, based on standardized coefficients?
⚠ Common exam trap
The trap here is that candidates mistakenly compare unstandardized coefficients or p-values instead of standardized coefficients, leading them to choose a variable like bathrooms or bedrooms that appears significant but has a weaker standardized effect.
Answer choices
Why each option matters
Answer the question above first, then reveal the full breakdown to understand why each option is right or wrong.
Correct answer & explanation
✓
sqft_living
Standardized coefficients (beta weights) allow comparison of the relative strength of independent variables by measuring the number of standard deviations the dependent variable changes per one standard deviation change in the predictor. In the regression output, sqft_living has the highest absolute standardized coefficient, indicating it has the strongest effect on price. The intercept is not an independent variable and its coefficient is not standardized for comparison.
Answer analysis
Option-by-option breakdown
For each option: why learners choose it and why it is or isn't the right answer here.
- ✗
bathrooms
Why it's wrong here
Standardised coefficients compare each predictor's effect in standard-deviation units, so the variable with the largest absolute beta wins; bathrooms is simply one candidate whose magnitude must be compared against the others. Selecting it without that comparison ignores the ranking the question demands, though it would be right if its beta were genuinely largest.
- ✓
sqft_living
Why this is correct
Standardised coefficients express each predictor's effect in standard-deviation units, so they are directly comparable across variables measured on different scales. The variable with the largest absolute standardised coefficient, sqft_living, therefore exerts the strongest effect on price.
- ✗
Intercept
Why it's wrong here
The intercept is the predicted price when every predictor equals zero, not an independent variable, so it carries no standardised beta for ranking effects. It is tempting because it appears in the coefficients table alongside the predictors, but it would only be cited when reporting the model's baseline value, not the strongest driver.
- ✗
bedrooms
Why it's wrong here
Bedrooms is only one of several predictors, and its standardised beta must be compared in absolute magnitude against the others before any ranking claim. Choosing it without that comparison ignores the actual axis of comparison. It would be correct only if its standardised coefficient were genuinely the largest in the output.
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