← VCE Data Analytics U3O1

Statistical modelling to make predictions

A rule built from past data, like a regression line, that uses the relationship between variables to estimate new values. A strong r makes the estimates more reliable.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 136

Understanding Statistical modelling to make predictions in VCE Data Analytics U3O1

What it does: The regression line is y = slope * x + intercept. Both are worked out from past data, then x = 5 is put in to estimate y. ABS gives the strength of r whether it is positive or negative. The closer it is to 1, the more reliable the model's estimates will be. The line lets you estimate new values. It shows a relationship, not proof of cause (correlation is not causation). Estimates inside the range of the data (interpolation) are safer. Going far outside the range assumes the pattern continues, which may not be true. Substitute x = 4: y = 5 × 4 + 40 = 60. Remember the model gives an estimate, not a guaranteed result.

Common mistakes: The regression line is y = mx + c. The slope m must be multiplied by x, then c added: estimate = m * 10 + c. FORECAST needs the known y values first, then the known x values. The ranges are swapped, so it should be =FORECAST(10, B2:B9, A2:A9).

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This module's key terms are also in a printable crossword (Modules 130–148) and word search (Modules 94–148).

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Learning
Duo
Which describes a statistical model such as a regression line?
A rule built from past data that estimates new valuesA list of the raw data with no pattern used
Matches
=FORECAST(C2:C9,B2:B9,5)
↓
The arguments are in the wrong order. The new x value must come first, then the known y values, then the known x values.
Applying
Meanings
Term
statistical model
Meaning
A rule built from past data, like a regression line, that uses the relationship between variables to estimate new values. A strong r makes the estimates more reliable.
Practice
=FORECAST(70,D2:D9,B2:B9)
Testing
Gaps
=(A10,B2:B9,A2:A9)
Check Answer
Spots
3c = INTERCEPT(B2:B9, A2:A9)
4estimate = m + 10 * c

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Quick Questions

1. Which describes a statistical model such as a regression line?
A. A rule built from past data that estimates new values ✓
B. A list of the raw data with no pattern used
A statistical model uses relationships in past data to estimate new values, for example y = mx + c.
2. A regression line is drawn through a scatter graph of study hours and test marks. What is it used for?
A. Proving that studying causes higher marks
B. Estimating the mark for a number of study hours not in the data ✓
The line lets you estimate new values. It shows a relationship, not proof of cause (correlation is not causation).
3. Which value of r would make estimates from a regression line most reliable?
A. r = 0.92 ✓
B. r = 0.08
The closer r is to +1 or -1, the stronger the relationship, so the estimates are more reliable. An r near 0 shows almost no linear relationship.
4. A model has r = -0.85. What can you say about it?
A. It is a strong negative relationship, so estimates are fairly reliable ✓
B. It is a weak relationship, so estimates are unreliable
The sign shows direction (negative) and the size 0.85 shows strength (strong). A strong r, positive or negative, supports reliable estimates.
5. Which spreadsheet formula estimates a new y value from a regression line?
A. =COUNTIF(B2:B9,8)
B. =FORECAST(8,B2:B9,A2:A9) ✓
FORECAST uses the line fitted to known x and y values to estimate a y value for a new x. COUNTIF only counts matching cells.

Match the Pairs

=CORREL(B2:B9,C2:C9) → Finds r, which shows how strongly two variables are related and so how reliable a regression line will be
=FORECAST(5,C2:C9,B2:B9) → Uses a regression line built from past data to estimate the y value when x is 5
A statistical model uses the slope and intercept of a regression line from past data to estimate a new value → =SLOPE(C2:C9,B2:B9)*5+INTERCEPT(C2:C9,B2:B9)
Before trusting a model's estimate, check that r shows a strong relationship in the past data → =ABS(CORREL(B2:B9,C2:C9))
=FORECAST(C2:C9,B2:B9,5) → The arguments are in the wrong order. The new x value must come first, then the known y values, then the known x values.
r = 0.1, so the regression line will give very reliable estimates → An r value near 0 shows a very weak relationship, so the estimates from the model are unreliable, not reliable.

Key Term

statistical model
A rule built from past data, like a regression line, that uses the relationship between variables to estimate new values. A strong r makes the estimates more reliable.

Fill in the Blanks

1. =FORECAST(A10,B2:B9,A2:A9)
Hint: Type the function that estimates a new y value from the regression line of past data.
2. =CORREL(A2:A9,B2:B9)
Hint: Type the function that finds r, the strength of the relationship, before trusting a model.
3. =SLOPE(B2:B9,A2:A9)
Hint: Type the function that gives the gradient of the regression line.
4. predicted = intercept + slope * x
Hint: Type the variable for the value where the regression line crosses the y axis.
5. =IF(ABS(D2)>=0.7,"Reliable","Weak")
Hint: Type the function that ignores the sign of r so strong negative values count as strong.

Spot the Error

Question 1
A r = CORREL(A2:A9, B2:B9)
B m = SLOPE(B2:B9, A2:A9)
C c = INTERCEPT(B2:B9, A2:A9)
D estimate = m + 10 * c
Line D — The regression line is y = mx + c. The slope m must be multiplied by x, then c added: estimate = m * 10 + c.
Question 2
A =FORECAST(10, A2:A9, B2:B9)
B =CORREL(A2:A9, B2:B9)
C =SLOPE(B2:B9, A2:A9)
Line A — FORECAST needs the known y values first, then the known x values. The ranges are swapped, so it should be =FORECAST(10, B2:B9, A2:A9).
Question 3
A r ← 0.92
B IF r >= 0.7 THEN
C OUTPUT "Unreliable estimate"
D END IF
Line C — An r of 0.92 is a strong correlation, so the estimates are reliable. The message should say "Reliable estimate".
Question 4
A =CORREL(A2:A9,B2:B9)
B =SLOP(B2:B9,A2:A9)
C =INTERCEPT(B2:B9,A2:A9)
Line B — The function name is misspelt, so the spreadsheet shows #NAME?. It should be =SLOPE(B2:B9,A2:A9).
Question 5
A hours ← 6
B mark ← 5 * hours + 40
C OUTPUT hours
Line C — The program should output the estimated value from the model (mark), not the input value (hours) that was used to make the estimate.

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