Can you show how to do this problem ?

Question

A scientist planted seeds in 4 sections of soil for an experiment. Not all of the seeds grew into plants.
TABLE

Section Size of section (Square feet) Number of plants
1 25 13
2 100 38
3 125 47
4 150 62
.explain or show how you determined your approximation.

.Let y be the number of plants expected to grow in x square feet. Write an equation the scientist could use to model the relationships between y and x.

Answer 1

If you plot the points on a graph you'll see the relationship is pretty linear. I used square feet as the independent variable and number of plants as the dependent variable.

 

The equation I got from a linear least-squares fit is

 

number of plants = 0.37*square feet + 2.3,

 

with an R-squared value of 0.98. If you cannot use "I plotted the data in Excel and added a trendline to the data, using Excel's LLQ function to determine the equation of the trendline," as how you determined your approximation, plot the data on your own graph paper by hand.

 

Then, draw your best-fit line through the data, without "forcing" a y-intercept through (0, 0). This is called the "graphic eyeball" technique, and is still state-of-the-art for fitting data from cumulative probability distributions on log-probit paper. (Software packages never weight the extreme points correctly.)

 

Your line will pass very slightly above the point at (25, 13), more above the points (100, 38) and (125, 47), and below (150, 62).

 

To get the line's slope, use m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are points on your trendline, preferably far apart. To get the intercept, extend your trendline to the y-axis.

 

Your values will approximate the equation obtained above, from Excel's LLQ function.

 

Eric M.

McMinnville OR