use data in table to write an equation four your trend line:
apparent temperature due to humidity at a room temperature of 72 degrees F
Humidity 0/20/40/60/80/100
apparent 64/67/70/72/74/76
temperature
possible answer for equation to trend line
(y= mx + B)
possible answer: y = 2/15x + 64
help...i don;t get it...can you explain step by step....why a possibility is 2/15x( I do get that b is the y intercept )
if y=mx+b, then when x=0
y = b
so, from the table,
y = mx+64
Now for every 20 increase in x, y increases 3 or 2. So, the slope could be somewhere between
y = 3/20 x + 64, which would be a bit high
and
y = 2/20 x + 64, which would be a bit low
Now,
3/20 = 9/60
2/20 = 6/60
2/15 = 8/60
So, y = 2/15 x + 64 could model the table, approximately
To find the equation for the trend line, you can use the method of linear regression. This involves finding the best-fitting line that represents the relationship between two variables, in this case, humidity (x-axis) and apparent temperature (y-axis).
Step 1: Set up the data
First, let's organize the given data in a table:
Humidity: 0 20 40 60 80 100
Apparent Temperature: 64 67 70 72 74 76
Step 2: Plot the data points
On a graph, plot the data points based on the values in the table. Use humidity as the x-axis and apparent temperature as the y-axis. This will help visualize the relationship between the variables.
Step 3: Determine the slope (m)
To calculate the slope (m), you'll need to find the change in y-values (Δy) divided by the change in x-values (Δx) between any two points. In this case, let's consider the points (0, 64) and (100, 76). The change in y-values is 76 - 64 = 12, and the change in x-values is 100 - 0 = 100. Therefore, the slope is Δy/Δx = 12/100 = 0.12.
Step 4: Determine the y-intercept (B)
To calculate the y-intercept (B), you can choose any point on the line. Let's use the point (0, 64). The y-intercept (B) represents the value of y when x equals zero. In this case, B = 64.
Step 5: Write the equation using slope-intercept form
Now that we have the slope (m = 0.12) and the y-intercept (B = 64), we can write the equation using slope-intercept form: y = mx + B.
Substituting the values we found:
y = 0.12x + 64
Simplifying the equation:
y = (12/100)x + 64
To make the numbers easier to work with, we can simplify further:
y = (3/25)x + 64
This equation represents the trend line that best fits the data points. It can be used to estimate the apparent temperature based on different levels of humidity.
Please note that this is just one possible equation for the trend line based on the given data points. Depending on the method or software used for regression analysis, you may get slightly different results.