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In a study relating the degree of warping, in mm, of a copper plate (y) to temperature in °C (x), the following summary statisti

kipiarov [429]

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 $Y=mx +b$ , 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:

$\sum_{i=1}^n (x_i -\bar x)^2 =98775$

$\sum_{i=1}^n (y_i -\bar y)^2 =19.4$

$\bar x =26.36$

$\bar y =0.5188$

n= 40 represent the sample size

$\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y) =796.94$

The total sum of squares is given by this formula:

$SST= \sum_{i=1}^n (y_i -\bar y)^2 =19.4$

And from the formulas for a simple regression, we need to calculate the slope for the regression like this:

$m=\frac{\sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)}{\sum_{i=1}^n (x_i -\bar x)^2}$

And if we replace the values given we have:

$m=\frac{796.94}{98775}=0.008068$

We have another useful equation in order to find the sum of squares for the regression, given by:

$SSR=m* \sum_{i=1}^n (x_i -\bar x)(y_i -\bar y)=0.008068*796.94=6.430$

And we know this equivalence:

$SST= SSR+SSE$

And solving for the sum of squares for the error we have:

$SSE=SST-SSR=19.4-6.430=12.97$

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

6 0

3 years ago

The graph of f(x) is show below.

vlada-n [284]

ANSWER

(2,2)

EXPLANATION

Since f(x) and its inverse function are symmetric about the line y=x, if (a,b) lies on the graph of f, then (b,a) must lie on f inverse.

The point (2,2) lies on f and the same time on f inverse.

The solution is a point that satisfies both equations.

Hence the correct choice is:

(2,2)

5 0

4 years ago

Read 2 more answers

List the steps used to solve the equation below.

pychu [463]

Answer:

- 1

Step-by-step explanation:

2x + 3 = x - 4

2x - x = - 4 + 3

x = - 1

The solution to the above equation is - 1.

4 0

3 years ago

The nature park has a pride of 7 lions and 9 cubs. The adults eat 9 pounds of meat each day and the cubs eat 4 pounds. Simplify

Blizzard [7]

Answer:

the answer to that question is 99

7 0

3 years ago

Suppose n(x)= 22 and n(y) is 13 what is the maximum number of elements X ∪Y can have ?

Nikolay [14]

The inclusion/exclusion principle states that

$|X\cup Y|=|X|+|Y|-|X\cap Y|$

That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).

Therefore, $|X\cup Y|$ will have the most elements when the sets $X$ and $Y$ are disjoint, i.e. $X\cap Y=\emptyset$ , which would mean the most we can can in this case would be

$|X\cup Y|=|X|+|Y|=22+13=35$

(Note that $n(X)=|X|$ denotes the cardinality of the set $X$ .)

3 0

4 years ago