Which represents a unit rate?
2 answers:
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Answer:
The error sum of squares is SSE=12.97
The regression sum of squares is SSR=6.430
The total sum of squares is SST=19.4
Step-by-step explanation:
Linear regression is a way "to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables)".
Regression estimates are "used to describe data and to explain the relationship between one dependent variable and one or more independent variables"
The linear model is given by the following equation , where y is the dependent variable, x the independent variable, m the slope and b the intercept.
For this case we have the following info given:
n= 40 represent the sample size
The total sum of squares is given by this formula:
And from the formulas for a simple regression, we need to calculate the slope for the regression like this:
And if we replace the values given we have:
We have another useful equation in order to find the sum of squares for the regression, given by:
And we know this equivalence:
And solving for the sum of squares for the error we have:
So then we have the final solutions:
The error sum of squares is SSE=12.97
The regression sum of squares is SSR=6.430
The total sum of squares is SST=19.4
Part A:
x + y = 9
4x + y = 6
To solve this system using substitution, begin by isolating either x or y in the first equation. I'll isolate x.
x + y = 9
x = 9 - y
Substitute this expression (9 - y) into the second equation for x and solve.
4x + y = 6
4(9 - y) + y = 6
36 - 4y + y = 6
36 - 3y = 6
-3y = -30
y = 10
To find x, substitute 10 for y into either of the original equations.
x + y = 9
x + 10 = 9
x = -1
Finally, check all work by substituting the x- and y-values into each original equation.
x + y = 9 --> -1 + 10 = 9 --> 9 = 9 --> True
4x + y = 6 --> 4(-1) + 10 = 6 --> -4 + 10 = 6 --> 6 = 6 --> True
The answer for Part A is x = -1 and y = 10; (-1, 10).
Part B:
For graphing, it's easier to get the equations into slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To get our equations into slope-intercept form, we must simply isolate y.
x + y = 9
y = 9 - x
y = -x + 9
4x + y = 6
y = 6 - 4x
y = -4x + 6
Now that we have our slope-intercept equations, we can easily graph them, since their slopes and y-intercepts are readily visible.
Let's start with the y-intercepts. They are (0, 9) and (0, 6). You can plot those points on the graph.
Now, the slopes. The slope of the first line is -1, this means it declines. To plot this, start where you plotted the y-intercept, count one unit down, and then one unit to the right, and plot that point. Continue doing that and connect the dots, and you will have plotted the first line. The slope of the second line is -4, so it also declines. For this line, count four units down, and then one to the right and plot that point. Likewise, continue this and connect the coordinates, and you will have your line. (See attachment for graph.)
The lines do indeed intersect at (-1, 10); our answer is verified by graphing.
