Worksheet 2 on scatter plots and line of best fit, featuring data analysis and graphing exercises.

Here are the solutions to the problems on the worksheet, worked out step by step.

1. Correlation Type
The problem states that as training ($x$) increases, the number of calls ($y$) also increases. When two variables move in the same direction (both go up), it is called a positive correlation.

2. Scatter Plot Sketch
To sketch this, you would draw a graph with "Year" on the bottom axis and "Population" on the side axis. You would place dots at these coordinates:
* (1970, 65)
* (1980, 55)
* (1990, 45)
* (2000, 35)
* (2001, 25)
* (2002, 15)
* (2003, 5)

3. Line of Best Fit
If you connect these points with a straight line, it will be a diagonal line going downwards from left to right. It passes perfectly through all the points because the pattern is consistent.

4. Type of Correlation for Graph
Looking at the data in question 2, as the years go forward (increase), the population numbers go down (decrease). When one variable goes up and the other goes down, this shows a negative correlation.

5. Calculate the Slope
We need to find the slope using the points $(45, 1990)$ and $(65, 2002)$.
*Note: In this specific question, the order of coordinates seems swapped compared to standard $(x,y)$ notation where $x$ is usually time/year. However, looking at the previous questions, Year is the independent variable ($x$) and Population is dependent ($y$). Let's look closely at the prompt: "points (45, 1990) and (65, 2002)". Usually, points are written $(x,y)$. If we assume standard $(x,y)$ format:*
* Point 1: $x_1 = 45$, $y_1 = 1990$
* Point 2: $x_2 = 65$, $y_2 = 2002$

Formula for slope ($m$):
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

$$m = \frac{2002 - 1990}{65 - 45}$$
$$m = \frac{12}{20}$$
$$m = 0.6$$

*(Self-Correction/Alternative Interpretation: In the context of the table in Q2, 1990 and 2002 are Years, and 45 and 65 are Populations. If the question implies calculating the rate of change of Year relative to Population, the answer is 0.6. However, typically we calculate slope as Change in Y / Change in X. If we treat Year as X and Population as Y based on the table, the points would be $(1990, 45)$ and $(2002, 65)$—but wait, the table says in 1990 pop was 45 and in 2002 pop was 15. The points given in Q5 $(45, 1990)$ and $(65, 2002)$ do not match the data in the table in Q2 exactly (Table says 2002 is pop 15, Q5 uses pop 65? Or is 65 the year? No, 65 is likely population from 1970). Let's stick strictly to the math requested in Q5 using the numbers provided in the text of Q5, ignoring the table data mismatch.)*

Using the explicit numbers in Question 5:
Slope = $\frac{2002 - 1990}{65 - 45} = \frac{12}{20} = 0.6$

6. Equation of the Line
Using the slope $m = 0.6$ and point $(45, 1990)$:
Equation form: $y - y_1 = m(x - x_1)$
$y - 1990 = 0.6(x - 45)$
$y - 1990 = 0.6x - 27$
$y = 0.6x + 1963$

7. Predict Population in 2003
*Note: This question refers back to the Table in Question 2.*
Looking at the table provided in Question 2, the column for the year 2003 already lists the population.
The value listed under 2003 is 5 (which represents 5,000 people).

8. Correlation of the Bottom Graph
The graph shows "Time" on the bottom and "Distance travelled" on the side. As Time increases (moves right), the Distance dots go lower (move down). This indicates a negative correlation.

9. Predict Distance at Time = 2
Looking at the graph for Question 8-10:
Find "2" on the horizontal Time axis. Look up to find the red dot.
The red dot aligns with 60 on the vertical Distance axis.
Answer: 60

10. Predict Distance at Time = 3
Find "3" on the horizontal Time axis. Look up to find the red dot.
The red dot aligns with 50 on the vertical Distance axis.
Answer: 50

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Final Answer:
1. Positive correlation
2. (Sketch requires plotting points: 1970/65, 1980/55, 1990/45, 2000/35, 2001/25, 2002/15, 2003/5)
3. (Draw a straight line connecting the plotted points diagonally downward)
4. Negative correlation
5. 0.6
6. y = 0.6x + 1963
7. 5 (or 5,000)
8. Negative correlation
9. 60
10. 50