Astudent 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) 9 14 19 24 29 34 39 44 49 54
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.
part b: write an equation which best fits the data.
part c: what does the slope and y-intercept of the plot indicate about the plant?

answer:

a) correlation coefficient = 1

b) equation of line of best fit; y = 5x +   9

c)

the slope of the plot from the above equation is 5. this implies that for every additional hour of sunlight, the plant grows 5 cm taller.

on the other hand, the y-intercept is 9. this will imply that the plant will grow up to 9 cm in the absence of sunlight.

step-by-step explanation:

in order to analyze the data we first import it into a software that can be used for data analysis. i imported the data into ms. excel which is the most basic of them all.

a)

we use the following function to calculate the correlation coefficient between the number of hours of sunlight that the plant receives and the height to which it grows;

=correl(x,y)

where x and y are the data arrays. we then press enter to calculate the value. ms. excel returns a value of 1 as the coefficient of correlation between x and y. this implies perfect association between the number of hours of sunlight and the height to which the plant grows.

b)

to determine the equation of the line of best fit, we do the following in ms. excel;

we highlight the entire data array and go to the insert tab where we insert a   (x, y) scatter-plot to our data. the next step is to add a trend line to our chart using the add chart element feature and check on the display equation on chart option.

the equation of the line of best fit of the data is returned as;

y = 5x +   9

c)

the slope of the plot from the above equation is 5. this implies that for every additional hour of sunlight, the plant grows 5 cm taller.

on the other hand, the y-intercept is 9. this will imply that the plant will grow up to 9 cm in the absence of sunlight.

we need the options

step-by-step explanation:

the answer is y = 11.54

hope this : )