SCSA Mathematics Applications Bivariate data analysis

This option describes the marginal percentage of all students who passed Electrical. The table provides conditional percentages based on Machinery results, not the total population distribution.

This option describes the marginal percentage of all students who failed Machinery. The value 10% represents a specific intersection of results relative to a subgroup, not the total proportion of students failing Machinery.

This interprets the condition in reverse (conditioning on the row). Since the rows do not sum to 100% ($80\% + 10\% \neq 100\%$), the percentages are not based on the group of students who achieved satisfactory in Electrical.

A negative association requires a correlation coefficient less than zero ($r < 0$), but the given value is $0.23$.

A strong positive association typically corresponds to an $r$ value closer to $1$ (e.g., $r > 0.7$), whereas $0.23$ represents a weak relationship.

This option describes a correlation coefficient close to $-1$, but the given value is positive and indicates a weak relationship.

This result comes from dividing the sum by $n$ ($10$) instead of $n-1$ ($9$). The formula for the sample correlation coefficient uses $n-1$ degrees of freedom.

This option has the incorrect sign and uses the incorrect divisor ($n=10$). Since the sum of the products is negative, the correlation coefficient must be negative.

This option has the incorrect sign. The correlation coefficient $r$ always shares the same sign as the sum of the standardized products, which is given as negative.

These are typically treated as two categorical variables associated with a car, rather than a clear explanatory variable driving a response variable.

This example describes an association between a category and a summary statistic, rather than a direct explanatory-response relationship between variables.

This option lists the response variable (plant growth) first and the explanatory variable (amount of fertiliser) second, which is the reverse of the order requested.

Vehicle age is the explanatory variable because it predicts the distance travelled, not the response variable.

Response variables are plotted on the vertical axis ($y$-axis), not the horizontal axis.

Distance travelled is the response (dependent) variable because it depends on the age of the vehicle, not the explanatory variable.

Incorrect. This value does not match the result of the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Incorrect. This is the reciprocal of the slope, incorrectly calculated by dividing the change in $x$ by the change in $y$ ($\frac{6.37}{-22.3} \approx -0.29$).

Incorrect. The data shows that as energy intake increases, birth rate decreases, meaning the slope must be negative.

Incorrect. This value is positive, but the inverse relationship between energy intake and birth rate requires a negative slope.

This reverses the variables; $R^2$ measures the proportion of variation in the response variable ($y$) explained by the explanatory variable ($x$), not the variation in $x$ explained by $y$.

$R^2$ measures the proportion of the variation in the observed response values ($y$), not the predicted outcomes, that is explained by the model.

This refers to the variation in the explanatory variable ($x$), whereas $R^2$ specifically measures the explained variation in the response variable ($y$).

Incorrect. Substituting 31 into the equation yields $67.5 - 1.27 \times 31 = 28.13$, which is not the closest value to 25.6.

Incorrect. Substituting 32 into the equation yields $67.5 - 1.27 \times 32 = 26.86$, which is not the closest value to 25.6.

Incorrect. Substituting 34 into the equation yields $67.5 - 1.27 \times 34 = 24.32$, which is not the closest value to 25.6.

This is incorrect because a 'negative' relationship implies that as one variable increases, the other decreases. Additionally, observational data establishes association, not necessarily causation.

This is incorrect because correlation does not imply causation. While the variables move together, it is likely a third variable (like hot weather) causes both to increase, rather than ice blocks causing fan sales.

This is incorrect because a negative association describes an inverse relationship where one variable decreases as the other increases, contradicting the observation that both increase.

This describes a discrete variable, which is defined by having a countable number of possible values, rather than a confounding variable.

A value that remains constant is simply a constant or a controlled variable, whereas a confounding variable varies and affects the outcome.

This describes the explanatory (or independent) variable, which is the specific factor the researcher is studying to see if it causes a change.