Free QCE General Mathematics Flashcard Review
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What is Pearson's r when the correlation is perfect positive?
Pearson's r = +1.0 indicates perfect positive linear correlation: as x increases, y increases in a perfectly linear relationship.
What is Pearson's r when the correlation is perfect negative?
Pearson's r = −1.0 indicates perfect negative linear correlation: as x increases, y decreases in a perfectly linear relationship.
What does Pearson's r ≈ 0 indicate about the linear relationship?
Pearson's r ≈ 0 indicates no linear correlation; variables are not linearly related (though a non-linear relationship may exist).
What strength threshold does |r| > 0.8 represent?
|r| > 0.8 indicates a strong linear correlation (positive if r > +0.8, negative if r < −0.8).
What strength threshold does 0.5 < |r| ≤ 0.8 represent?
0.5 < |r| ≤ 0.8 indicates a moderate linear correlation; pattern is evident but with noticeable scatter around the line.
What strength threshold does 0.3 < |r| ≤ 0.5 represent?
0.3 < |r| ≤ 0.5 indicates a weak linear correlation; some association present but considerable scatter.
What strength threshold does |r| ≤ 0.3 represent?
|r| ≤ 0.3 indicates negligible or very weak linear correlation; little to no linear association.
What does the sign of r indicate?
The sign of r indicates direction: positive r means both variables increase together; negative r means one increases as the other decreases.
How do you interpret R2 = 0.85?
R2 = 0.85 means 85% of the variance in the dependent variable is explained by the independent variable in the regression model; 15% is unexplained.
What is the relationship between Pearson's r and R2?
R2 = (Pearson's r)2. For example, if r = 0.9, then R2 = 0.81; R2 is always non-negative and ranges from 0 to 1.
What does the gradient (slope) represent in a regression equation y = a + bx?
The gradient b represents the change in y for each unit increase in x; interpreted in context (e.g., 'for every 1 kg increase in mass, height increases by 0.5 cm').
What does the y-intercept (a) represent in the regression equation y = a + bx?
The y-intercept a is the predicted value of y when x = 0; must be interpreted in context (often has no practical meaning if x = 0 is outside the data range).
What are the four steps to calculate a centred moving average for even-period data?
1) Calculate simple moving averages of the given period. 2) Calculate moving averages of the moving averages (2-point average). 3) These results are centred between time periods. 4) Assign the centred values to the middle time point of the original moving average span.
For a 4-period centred moving average, how many data points are lost?
Three data points are lost: one at the start (before the first 4-point average can be calculated) and two at the end (because the 2-point average of moving averages requires pairs).
Write the formula for a seasonal index for a specific quarter/season.
Seasonal index = (actual value for that period) ÷ (centred moving average for that period); often expressed as a decimal or percentage.
How do you deseasonalise a time series value?
Deseasonalised value = (actual value) ÷ (seasonal index for that season); this removes seasonal fluctuation to reveal underlying trend and irregular components.
Write the explicit rule for an arithmetic sequence.
t_n = t1 + (n − 1)d, where t_n is the nth term, t1 is the first term, n is the term number, and d is the common difference.
Write the recurrence relation for an arithmetic sequence.
t_n = tn−1 + d, where each term equals the previous term plus the common difference d.
Write the explicit rule for a geometric sequence.
t_n = t1 × r^(n−1), where t_n is the nth term, t1 is the first term, r is the common ratio, and n is the term number.
Write the recurrence relation for a geometric sequence.
t_n = r × tn−1, where each term equals the previous term multiplied by the common ratio r.