Question

A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table below shows the data:

Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31

Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)

Part B: Write a function which best fits the data. (3 points)

Part C: What does the slope and y-intercept of the plot indicate about the plant

Answer 1

Explanation:

there is a direct correlation between the hours of sunlight and the height of the plant.

a delta of 1 hour sunlight results consistently in a growth of 3 cm. there is not a single point in the set of data that deviates from this.

therefore, the function for the height of the plant based on the number of sunlight received is

y = 3x + 4

as every hour of sunlight (x) results in an additional growth of 3cm. and we are starting with a plant that is already 4 cm tall at the beginning (x=0).

the y-intercept is the first data point (x=0) and shows y=4.

the slope is 3 (or 3/1 as y/x ratio) indicating that with one hour of sunlight the plant grows an additional 3 cm.

and as mentioned, we started with a plant already 4cm tall.

Answer 2

see below

Explanation:

Part A

Notice that for each increase of 1 in x, there is an increase of 3 in y

There is a correlation between the amount of sunlight and the height of the plant

Part B

The slope in change in y over change in x

m = 3/1 = 3

y= mx+b

y = 3x+b

The y intercept is when x =0 so b = 4

y = 3x+4

Part C

With no sunlight the plant is 4 cm tall. As the plant gets more sunlight, the plant grows at 3 cm per hour of sunlight.