Question

The table shows the number of birds seen by a bird watcher for each day, where x is the temperature that day in degrees Celsius and y is the number of birds seen.
Question 2: What was the linear correlation coefficient and what does it indicate about the data? (Hint: what is r equal to)

Answer 1

The correlation coefficient indicates the strength of the relationship

between the variables.

Question 15;

• The equation of best fit is; y = 0.83·X + 2.63

Question 2:

• The linear correlation coefficient is R ≈ 0.9871

• There is a strong correlation between the temperature and the number of bird seen.

Question 17:

• Blank # 1: 18 birds

• Blank # 2: Interpolation

Question 18:

• Blank # 1: 4°C

• Blank # 2: Extrapolation

Question 19:

• The number of birds seen when the temperature is 30°C are 27 birds

Reasons:

Question 15

Plotting the given values of temperature, x and number of birds seen y on

MS Excel gives the equation of best fit for the data as follows;

• Plot the given data using the Insert → Chart → Scatter plot option

• Under the Chart design tab, select Add Chart Element.

• Move the mouse down the drop down menu to the Trendline option

• Select More Trendline Options from the Trendline menu

From the dialogue box that displays on the right select;

• Display Equation on chart.

• Display R-squared on chart.

The equation of best fit is; y = 0.83·X + 2.63

Question 2:

The square of the correlation coefficient, R² = 0.9744

Which gives, R = √(0.9744) ≈ 0.9871

The high positive value of the correlation coefficient indicates that there is a correlation between the temperature and the number of bird seen.

Question 17:

When the temperature is 19 degrees, we have;

The number of birds seen, y = 0.83 × 19 + 2.63 = 18.4

When the temperature is 19 °C, the number of birds seen are 18 birds.

Blank # 1: 18 birds

Blank # 2: Interpolate

Question 18:

When only 6 birds are seen, we have;

6 = 0.83·X + 2.63

$X = \dfrac{6 - 2.63}{0.83} \approx 4.06$

When the number of birds seen is 6 birds, the temperature will be

approximately 4°C.

Blank # 1: 4°C

Blank # 2: Extrapolation; The values given and found are outside the given

range of values.

Question 19:

When the temperature is 30°C, we have;

y = 0.83 × 30 + 2.63 ≈ 27.53

The number of birds seen when the temperature is 30°C are 27 birds.

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