Problem 1
Part (a)
It is possible to find the equation of the line of best fit by hand, but it's much more efficient to use technology. That could mean a graphing calculator, an online tool, or some computer software installed. I'm going to use GeoGebra. Specifically, I'm using the "FitLine" command to find the regression line.
The equation of line of best fit is y = -2.45x + 11.83
There's not much to say in terms of steps, since it's basically a calculator problem. Doing this by hand would take a lot longer than it should be.
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Part (b)
Plug in x = 2.3 and evaluate
y = -2.45x + 11.83
y = -2.45*2.3 + 11.83
y = 6.195
Answer: 6.195
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Part (c)
We'll compare the result from the previous part (6.195) to the y value in the table (6.2)
The difference is 6.2 - 6.195 = 0.005
This means the estimated value is off by 0.005 and this is an underestimate (since 6.195 is smaller than 6.2)
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Problem 2
To be perfectly honest, I'm not sure what's going on here. It seems like there's missing context to the problem. Perhaps a data table that got cut off or this is referring to a previous problem.
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Problem 3
Recall that y = mx+b is the slope intercept form
m = slope
b = y intercept
We simply read off the values of the given equation y = 0.404x - 5.18 to see that 0.404 is the slope and -5.18 is the y intercept
The slope tells us that each time x goes up by 1, y will increase by an estimated amount of 0.404; this represents the unit rate or speed. In this context, it means the height goes up by about 0.404 cm per day. This is an estimated value because the regression line itself is a collection of estimated points.
The y intercept is where the graph crosses the y axis. It always occurs when x = 0. The x refers to the day number. Day 0 is basically the starting day. So the y intercept being -5.18 means the estimated height is -5.18 cm on the starting day. At first glance, it might not seem possible to have a negative height. But simply think of negative heights as below ground level, much like how the negative y values are below the x axis.
In other words, the plant is estimated to start off at about 5.18 cm below ground level. This is a reasonable assumption because the seed is buried into the ground (assuming at this level more or less) and it then grows upward.
