The estimated regression equation for a model involving two independent variables and 10 observations follows. Here SST = 6,724.125, SSE = 507.75, sb 1= 0.0813, and sb 2= 0.0567. y ^ = 29.1270 + 0.5906x1 + 0.4980x2
a. Interpret the regression coefficients in this estimated regression equation
-A one-unit increase in x1 will lead to a 0.5906 unit increase in y . A one-unit increase in x2 will lead to a 0.498 unit increase in y.
b. Predict y when x1 = 180 and x2 = 310
-289.82
c. Find SSR
-6,216.375
d. Compute R2
-0.924
e. Compute
f. Compute MSR
g. Compute MSE
h. Use the F test to determine the overall significance of the relationship among the variables. Use α = 0.05.
i. Perform a t test for the significance of x1. Use a 0.05 level of significance.
j. Perform a t test for the significance of x2. Use a 0.05 level of significance.
k. Construct a 95% confidence interval for the coefficient of x2.
Answers
a. The computed regression equation's regression coefficients, which hold the other independent variable constant, show the impact of each independent variable on the dependent variable. Y will grow by 0.5906 units for every unit increase in x1 and by 0.498 units for every unit increase in x2, respectively.
b. The regression equation can be changed to predict y for the cases when x1 and x2 are 180 and 310, respectively: y = 29.1270 + 0.5906 * 180 + 0.4980 * 310 = 29.1270 + 105.208 + 156.38 = 290.82
c. The sum of squares resulting from regression (SSR) is denoted by the formula: SSR = _(i=1)n (y i - y)2.
SSR = 6,216.375.
d. R2 = SSR / SST is how it is calculated.
R2 = 6,216.375 / 6,724.125 = 0.924 e is the result of substituting the supplied values. A measurement of the overall significance of the link between the variables is the F statistic. The calculation is:
f. The following equation yields the mean square due to regression (MSR):
MSR is calculated as SSR / (r - 1), where r is the total number of independent variables. MSR = 6,216.375 / (2 - 1) = 6,216.375 / 1 = 6,216.375 is the result of substituting the provided numbers.
g. MSE = SSE / (n - r - 1), where n is the number of observations and r is the number of independent variables, is the formula for the mean square due to error (MSE).
MSE = 507.75 / (10 - 2 - 1) = 507.75 / 7 = 72.53. With (r - 1) and (n - r - 1) degrees of freedom, we must compare the derived F statistic to the crucial value of F at alpha = 0.05 in order to utilize the F test to assess the overall significance of the association between the variables at a significance level of alpha = 0.05.
The crucial value can be found via of F, we can employ a critical value table or a statistical software program. The critical value of F is roughly 3.35 when alpha = 0.05 and the degrees of freedom are (r - 1) = (2 - 1) = 1 in the numerator and (n - r - 1) = (10 - 2 - 1) = 7 in the denominator.
The numbers for MSR and MSE can be substituted to get the following result: F = MSR/MSE = 6,216.375 / 72.53 = 85.24
The estimated F statistic (85.24) is higher than the threshold value of 3.35, which allows us to reject the null hypothesis that there is no association between the variables at alpha = 0.05. This shows a meaningful relationship between the dependent variable and at least one of the independent variables.
i. We must compare the t statistic for x1 to the crucial value of t at alpha = 0.05 with (n - r - 1) degrees of freedom in order to conduct a t test for the significance of x1 at an alpha = 0.05 significance level. As stated by the formula: t = b1 / sb1
where b1 is the regression coefficient for x1 and sb1 is the coefficient's standard error. T = 0.5906 / 0.0813 = 7.26 is the result of substituting the supplied values.
Statistical software or a table of critical values can both be used to determine the critical value of t. The critical value of t at alpha = 0.05 with (n - r - 1) = (10 - 2 - 1) = 7 degrees of freedom is roughly 2.365.
The estimated t statistic (7.26) exceeds the critical value of 2.365, hence the null hypothesis that the coefficient for x1 is not substantially different from zero at alpha = 0.05 can be rejected.
j. To run a t test to determine whether x2 is significant atWith (n - r - 1) degrees of freedom and a significance level of alpha = 0.05, we must compare the t statistic for x2 to the critical value of t. The formula for the t statistic for x2 is: t = b2 / sb2, where b2 is the x2 regression coefficient and sb2 is the coefficient's standard error. When the specified values are substituted, the following results are produced:
t = 0.4980 / 0.0567 = 8.79
Statistical software or a table of critical values can both be used to determine the critical value of t. The critical value of t at alpha = 0.05 with (n - r - 1) = (10 - 2 - 1) = 7 degrees of freedom is roughly 2.365.
As a result of the calculated t statistic (8.79) exceeding the crucial value of 2.365, we
can disprove the null hypothesis that the coefficient for x2 at alpha = 0.05 is not statistically different from zero.
k. The t statistic and the coefficient's standard error can be used to create a 95% confidence interval for the coefficient of x2. B2 +/- t * sb2 yields the confidence interval.
The values are replaced to yield: 0.4980 +/- 2.365 * 0.0567 = (0.3778, 0.6182)
This suggests that we have a 95% confidence that the true value of the x2 coefficient falls inside the given range (0.3778, 0.6182).
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Related Questions
Thank u so much I’ll award brainliesttttt
Answers
Answer:
JZF
Step-by-step explanation:
when JZF and HZJ are added together to make 180 degrees
this is significant because when a angle is supplementary both angles must add up to 180 degrees
What does modal,median and mean, mean
Answers
Answer:
Mode is the number that occurs the most in the data
the median is when you line up all the numbers in order and the median is the middle one
mean is the average: add all the numbers in the data together and then divide it by the amount of numbers
what is 11/2 times 1/3 as a fraction
Answers
Answer:
11/2 times 1/3 is 11/6
Step-by-step explanation:
11/2 times 1/3,
We have to multiply the numerators and denominators,
\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)
hence we get 11/6
find the greatest and least number from 5,0,8,9 and 7
Answers
Answer:
Greatest number: 98750Least number: 5789Explanation:
To find the greatest number with the following values, we must arrange the numbers in descending form.
=> We can clearly tell that the numbers in descending form is 9 > 8 > 7 > 5 > 0
Hence, the greatest number with the following numbers (5,0,8,9, and 7) will be 98750.
__________________________________________________To find the least number with the following values, we must arrange the numbers in ascending form.
=> We can clearly tell that the numbers in ascending form is 0 < 5 < 7 < 8 < 9
Hence, the least number with the following numbers (5,0,8,9, and 7) will be 5789
95 to 155 as a percentage
Answers
Answer:
61.290322580645% or 61%
Step-by-step explanation:
I put your question into a percentage calculator and got this for the answer. Wish you luck.
Answer:
Convert the decimal to a percentage by multiplying the decimal by 100
9515500%
Step-by-step explanation:
don't know if this the answer your looking for.
where RS = 6y + 2, ST = 2y + 7, and RT = 13y - 21.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete but a possibility is that the given parameters are points on a straight line.
I'll answer base on that assumption.
\(RS = 6y + 2\)
\(ST =2y + 7\)
\(RT =13y -21\)
To solve for y, we have that:
\(RT = RS + ST\)
This gives:
\(13y - 21 = 6y + 2 + 2y + 7\)
Collect Like Terms
\(13y - 6y - 2y = 21 +2+7\)
\(5y = 30\)
Divide both sides by 5
\(y = 6\)
To get the measure of each line. Substitute 6 for y in
\(RS = 6y + 2\)
\(ST =2y + 7\)
\(RT =13y -21\)
\(RS = 6 * 6 + 2 = 36 + 2 = 38\)
\(ST = 2*6 + 7 = 12 +7 = 19\)
\(RT = 13*6 - 21 = 78 - 21 = 57\)
Select ALL of the solutions of the following system of linear inequalities below.
Answers
The solutions of the system of inequalities are:
(0, 3)
(6, 2)
How to find the solutions of the system?Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).
And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.
Then the points that are solutions are:
(0, 3)
(6, 2)
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(40 POINTS!!) solve for x
Answers
Answer:
do 13+7 you will have your answer. (go down for answer)
Step-by-step explanation:
its 20
HELP ME PLEASEEEE INSTANTLY
Answers
The solution of the given inequality is -2(2/3) < c < 5 (1/3) which is the first option.
We are given the inequality:-
I3c - 4I < 12
We have to find the solution of the given inequalities.
Let 3c - 4 ≥ 0
Hence,
3c - 4 < 12
3c < 16
c < 16/3 = 5 (1/3)
c < 5 (1/3)
Let 3c - 4 < 0
Hence,
-3c + 4 < 12
-8 < 3c
-8/3 = -2(2/3) < c
-2(2/3) < c
Hence, we can write,
-8/3 = -2(2/3) < c
-2(2/3) < c < 5 (1/3)
Hence, the solution is Option A.
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What is the solution to this equation?
7x-3(x-6)= 30
A. X= 3.
B. x = 12
C. X= 9
D. x=6
Answers
Answer:
A
Step-by-step explanation:
To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:
7x - 3(x-6) = 30
7x - 3x + 18 = 30
4x + 18 = 30
Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:
4x + 18 - 18 = 30 - 18
4x = 12
Finally, we can solve for x by dividing both sides by 4:
4x/4 = 12/4
x = 3
Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.
How can u find a geometry-big circle mAB=56 mBC=59 mCD=63 mDE=63 mEF= 31
Answers
To find the measure of the geometry-big circle, we need to sum up the measures of all the arcs around the circle.
We are given the following measures:
\(\sf\:m\angle AB = 56 \\\)
\(\sf\:m\angle BC = 59 \\\)
\(\sf\:m\angle CD = 63 \\\)
\(\sf\:m\angle DE = 63 \\\)
\(\sf\:m\angle EF = 31 \\\)
To find the measure of the geometry-big circle, we add up these measures:
\(\sf\:m\angle AB + m\angle BC + m\angle CD + m\angle DE + m\angle EF \\\)
Substituting the given values:
\(\sf\:56 + 59 + 63 + 63 + 31 \\\)
Simplifying the expression:
\(\sf\:272 \\\)
Therefore, the measure of the geometry-big circle is 272.
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
please i’ll fail if i don’t get this right. please i’ll give brainlyist The current temperature of 15°F below zero is 18°F below the high temperature of the day. What is the high temperature for the
day?
OA. 5°F
ов. 33°F
OC. 3°F
OD. 33°F
Answers
Answer:
I think its C
Step-by-step explanation:
What is the volume of the composite figure
Answers
Answer:
291
Step-by-step explanation:
2*2*2=8*2=16
16+(11*5*5)=291
Answer:
291cm^3
Step-by-step explanation:
11×5×5=275cm^3
2×2×2=8cm^3
8cm^3 + 8cm^3= 16cm^3
275+16=291cm^3
Find the product. (-10) • (-10) • (-10)
Answers
Answer:
-1000
Step-by-step explanation:
-10 times -10 makes 100 as negative cancel each other
100 times -10 make -1000
Answer:
-1000
Step-by-step explanation:
-(10x10x10)
-10^3
-1000
The length of a living room is 12 feet and its width is 10.5 feet. The length of the room is being expanded by x feet.
A. Write an expression to represent the new area of the living room in square feet.
B. Expand the expression.
Answers
Answer:
A) A= 10.5(12 +x)
B) A= 10.5x +126
Step-by-step explanation:
A) Length of living room= 12 ft
Width= 10.5 ft
Since the length expanded by x ft,
New length of living room= (12 +x) ft
Area= length ×width
Let the new area of the living room be A ft².
A= 10.5(12+x)
B) To expand the expression, multiply 10 to each term and constant in the bracket on the right hand side of the equation.
A= 10.5(12 +x)
A= 10.5(12) +10.5x
A= 126 +10.5x
Complete the statements below about the area of the red rectangle.
Answers
Each red block has area of \(\frac{7}{12}\) square unit.
The area of the red rectangle is = \(\frac{7}{8}\)× \(\frac{2}{3}\) = \(\frac{7\times 2}{8\times 3}\) = \(\frac{7}{12}\) square unit.
What is area of rectangle?
The area of a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Here the given rectangle measures are,
Length of the rectangle = \(\frac{7}{8}\)
Breadth of the rectangle = \(\frac{2}{3}\)
Now area of the rectangle = length × breadth
=> A = lb
=> A= \(\frac{7}{8}\)× \(\frac{2}{3}\) = \(\frac{7\times 2}{8\times 3}\) = \(\frac{7}{12}\) square unit.
Hence each red block has area of \(\frac{7}{12}\) square unit.
The area of the red rectangle is = \(\frac{7}{8}\)× \(\frac{2}{3}\) = \(\frac{7\times 2}{8\times 3}\) = \(\frac{7}{12}\) square unit.
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Which expression is equivalent to 5y^3/(5y)^-2
Answers
Answer:
5^3 y^5
125 y^5
Step-by-step explanation:
5y^3/(5y)^-2
Distribute the exponent in the denominator
5y^3/(5 ^-2 y^-2)
A negative exponent in the denominator brings it to the numerator
5y^3 5 ^2 y^2
Combine like terms
5 * 5^2 * y^3 5^2
We know that a^b * a^c = a^(b+c)
5^(1+2) * y^( 3+2)
5^3 y^5
125 y^5
The sum of two numbers is 130 and their difference is 34. Let x be the first number and y be the second
number. Set up a system of equations and use the elimination method to find the numbers. You must
show your work.
Answers
Answer:
the two numbers are 82 and 48
Step-by-step explanation:
let the first number = x
let the second number = y
according to the given conditions:
x + y = 130 --------------(1)
x - y = 34 -----------------(2)
by using the elimination method we add both equations (1) and (2) and the resultant value is
2x = 164
x = 164/2 = 82
by substituting the value of x in eq (1)
82 + y = 130
y = 130-82
y = 48
3. Put the integers in order from smallest to greatest. a. -41; 54; -31; -79; 57 b. 43; -54; 44; -55; -37; 22; 52; -39; -43; -56; 18
please help asp
50 points
Answers
a. -79, -41, -31, 54, 57
b. -56, -55, -54, -43, -39, -37, 18, 22, 43, 44, 52
In both cases, I have put the integers in order from smallest to greatest by comparing each number and placing them in the correct order. Starting with the smallest number and moving to the largest.
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
Answers
If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
Given sample size be 300 and about 5% of the population has a particular genetic mutation.
We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.
Sample size=300
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation=\(\sqrt{np(1-p)}\)
Use the known values in the above formula.
Standard deviation=\(\sqrt{300*0.05(1-0.05)}\)
=\(\sqrt{14.25}\)
=3.77
Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.
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17 + 2.6b = 30
2.6b=30-17=
2.6b=13
b=13/2.6
2.6b/2.6=13/2.6
2.6b/2.6=5
b=5
How do I check this equation to see if it is correct?
Answers
Answer:
You insert 5 back into the equation
Step-by-step explanation:
17 +2.6b=30
17 +2.6(5)=30
17 +13=30
The large rectangle below represents one whole. What percent is represented by the shaded area? %
Answers
Answer:
Step-by-step explanation:
would help a lot if you show the picture or describe it very well.
A certain sum of money is divided among A, B, C in the ratio 2: 3 : 4. If A's share is RS. 20000, find the share of B and C.
Answers
Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.
Here,
Let the total sum of money be x.
Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:
2/9 * x = 20000
Multiplying both sides by 9/2, we get:
x = 90000
Now, we can find the shares of B and C as follows:
B's share = 3/9 * 90000 = 30000
C's share = 4/9 * 90000 = 40000
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Find the sum of the first 27 terms
of the arithmetic sequence.
First, fill in the equation.
a₁
= 5 and a27
Sn = 2/(a₁ + an)
Sn
=
[?]
2
+
=
83
Answers
Answer:
S₂₇ = 1188
Step-by-step explanation:
using the given formula for \(S_{n}\) , that is
\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )
with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then
S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188
What is the slope and the y-intercept of the following linear equation?
Answers
Answer:
wish i coul d help
Step-by-step explanation:
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
Answers
The length of the arcs are calculated to the nearest hundredth as:
12. 14.03 meters 13. 6.91 meters
How to Find the Length of an Arc?The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.
Length of arc XW:
∅ = m<XZW = 180 - 113
∅ = 67 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters
Length of arc XW:
∅ = m<YVU = 180 - 67 - 80
∅ = 33 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters
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Jazzmen's heart rate is 47 beats per minute. If this is her average heart rate, how
many times will her heartbeat in 50 years?
Answers
Answer:1235160000 beats
Step-by-step explanation:
There are 525600 minutes in a year
47*525600= 24703200
24703200*50= 1235160000
For each relation, decide whether or not it is a function.
Answers
Answer:
Relation 1 is not a function.
Relation 2 is a function.
Relation 3 is not a function.
relation 4 is a functtion.
Step-by-step explanation:
DOES ANYONE KNOW HOW TO FIGURE THESE QUESTIONS OUT??
(Geometry) There are 3 questions!
Answers
1.
These are Corresponding Angles, and thus by the Corresponding Angles Theorem, they are congruent.
\(4x-9=3x+29\\4x-9+9=3x+29+9\\4x=3x+38\\4x-3x=3x-3x+38\\x=38\)
2.
These are Same-Side Interior Angles and thus by the Same-Side Interior Angles Theorem they add up to 180°.
\(2x-26+7x+9=180\\9x-17=180\\9x-17+17=180+17\\9x=197\\9x/9=197/9\\x=21.9\)
3.
These are Alternate Exterior Angles and thus by the Alternate Exterior Angles Theorem they are congruent.
\(3x-2=2x+30\\3x-2+2=2x+30+2\\3x=2x+32\\3x-2x=2x-2x+32\\x=32\)
I am stuck on how to solve this problem. Any help is appreciated.
Answers
Answer:
y = 2/7x - 1
Step-by-step explanation:
You are trying to put it in the form y = mx + b where m is the slope and b is the y-intercept.
To start, find the slope by doing change in y (between the two points) divided by change in x (between the two points). This would be:
3 - (-3) (change in y) / 14 - (-7) (change in x)
= 6/21
= 2/7
So the slope is 2/7.
Then, you have the equation y = 2/7x + b.
Since you know the point (14, 3) works, you know x = 14 and y = 3 is a solution to the equation. You can plug in those values which would be:
3 = 2/7 * 14 + b
3 = 4 + b
-1 = b
So that means the equation is y = 2/7x - 1