Statistical modelling to make predictions

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Quick Questions

Shade in the A or B circle for each question.

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

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

3. Which value of r would make estimates from a regression line most reliable?

A r = 0.92

B r = 0.08

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

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)

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1=CORREL(B2:B9,C2:C9)		AFinds r, which shows how strongly two variables are related and so how reliable a regression line will be
2=FORECAST(5,C2:C9,B2:B9)		BThe arguments are in the wrong order. The new x value must come first, then the known y values, then the known x values.
3A statistical model uses the slope and intercept of a regression line from past data to estimate a new value		CUses a regression line built from past data to estimate the y value when x is 5
4Before trusting a model's estimate, check that r shows a strong relationship in the past data		DAn r value near 0 shows a very weak relationship, so the estimates from the model are unreliable, not reliable.
5=FORECAST(C2:C9,B2:B9,5)		E=ABS(CORREL(B2:B9,C2:C9))
6r = 0.1, so the regression line will give very reliable estimates		F=SLOPE(C2:C9,B2:B9)*5+INTERCEPT(C2:C9,B2:B9)

Definitions

statistical model

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=________(A10,B2:B9,A2:A9)

=______(A2:A9,B2:B9)

=_____(B2:B9,A2:A9)

predicted = _________ + slope * x

=IF(___(D2)>=0.7,"Reliable","Weak")

Spot the Error

Shade in the letter of the line that contains an 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

Question 2

A =FORECAST(10, A2:A9, B2:B9)

B =CORREL(A2:A9, B2:B9)

C =SLOPE(B2:B9, A2:A9)

Question 3

A r ← 0.92

B IF r >= 0.7 THEN

C OUTPUT "Unreliable estimate"

D END IF

Question 4

A =CORREL(A2:A9,B2:B9)

B =SLOP(B2:B9,A2:A9)

C =INTERCEPT(B2:B9,A2:A9)

Question 5

A hours ← 6

B mark ← 5 * hours + 40

C OUTPUT hours

Answer Key

Statistical modelling to make predictions

Section A: Quick Questions

A — A rule built from past data that estimates new values

B — Estimating the mark for a number of study hours not in the data

A — r = 0.92

A — It is a strong negative relationship, so estimates are fairly reliable

B — =FORECAST(8,B2:B9,A2:A9)

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

=FORECAST(A10,B2:B9,A2:A9)

=CORREL(A2:A9,B2:B9)

=SLOPE(B2:B9,A2:A9)

predicted = intercept + slope * x

=IF(ABS(D2)>=0.7,"Reliable","Weak")

Section E: Spot the Error

D — The regression line is y = mx + c. The slope m must be multiplied by x, then c added: estimate = m * 10 + c.

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).

C — An r of 0.92 is a strong correlation, so the estimates are reliable. The message should say "Reliable estimate".

B — The function name is misspelt, so the spreadsheet shows #NAME?. It should be =SLOPE(B2:B9,A2:A9).

C — The program should output the estimated value from the model (mark), not the input value (hours) that was used to make the estimate.