Consider the following sample data: x 10 7 20 15 18 y 22 15 19 14 15 Click here for the Excel Data File a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place
Answers
Answer:
a. Covariance between x and y = – 1.25
b. Correlation coefficient = – 0.07
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
Consider the following sample data:
x 10 7 20 15 18
y 22 15 19 14 15
Required:
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The explanation to the answer is now given as follows:
Note: See the attached excel file for the calculations of the sum of x and y, means of x and y, deviations of x and y, multiplications of deviations of x and y, and others.
a. Calculate the covariance between the variables. (Negative value should be indicated by a minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
In the attached excel file, we have:
N = Number of observations = 5
Mean of x = Sum of x / N = 70 / 5 = 14
Mean of y = Sum of y / N = 85 / 5 = 17
x - Mean of x = Deviations of x = see the attached excel file for the answer of each observation
y - Mean of y = Deviations of y = see the attached excel file for the answer of each observation
Multiplications of the deviations of x and y = (x - Mean of x) * (y - Mean of y) = see the attached excel file for the answer of each observation
Sum of the multiplications of deviations of x and y = Sum of ((x - Mean of x) * (y - Mean of y)) = –5
Since we are using a sample, we use (N – 1) in our covariance between x and y as follows:
Covariance between x and y = Sum of ((x - Mean of x) * (y - Mean of y)) / (N – 1) = –5 / (5 – 1) = –5 / 4 = –1.25
b. Calculate the correlation coefficient (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal place.)
The correlation coefficient can be calculated using the following formula:
Correlation coefficient = Covariance between x and y / (Sum of (x - Mean of x)^2 * Sum of (y - Mean of y)^2)^0.5 ………………… (1)
Where, from the attached excel file;
Covariance between x and y = –5
Sum of (x - Mean of x)^2 = 118
Sum of (y - Mean of y)^2 = 46
Substituting the values into equation (1), we have:
Correlation coefficient = –5 / (118 * 46)^0.5 = –5 / 5,428^0.5 = –5 / 73.6750 = – 0.07
Final answer:
The covariance between two variables can be calculated by first finding the mean of each dataset, subtracting the mean from each data point, multiplying the results for each pair of coordinates, summing these products to obtain the numerator. The denominator is obtained by subtracting one from the number of data points. The covariance is then the numerator divided by the denominator.
Explanation:
The term covariance is one of the key factors for understanding correlation between two variables. To calculate the covariance between the two given variables, we first need to calculate the mean of each set (x and y). After we've gotten the mean, we subtract the mean from each data point and multiply the results for each pair of x and y values. Summing these products will give us the numerator in the covariance calculation. The denominator is calculated by subtracting one from the total number of data points we have (n-1). So, the covariance is the sum we got from the numerator, divided by the denominator. Please don't forget to indicate if the covariance is negative, using a minus sign.
Learn more about Covariance here:
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Please help me in this! you get 30 points!
One numer is 17 more than another number the sum of the two numbers is 25 find the numbers
Answers
Sample space is made from all the possible outcomes that an event can have.
For example when tossing a coin, the possible outcomes are Head and Tail so the sample space will be {Head, Tail}.
Thus, option A is the correct answer
Answers
The number you're looking for is 10/9 or approximately 1.1111 when rounded to four decimal places.
You can represent this statement as an equation:
9x - 8 = 2
Here, "x" represents the unknown number. To solve for "x," first, add 8 to both sides of the equation:
9x - 8 + 8 = 2 + 8
This simplifies to:
9x = 10
Now, to isolate "x," divide both sides by 9:
9x/9 = 10/9
x = 10/9
So, the number you're looking for is 10/9 or approximately 1.1111 when rounded to four decimal places.
for such more question on decimal
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Answer:
10/9
Step-by-step explanation:
the question would be 9x - 8 = 2
which simplified you would get 9x = 10
dividing 9 from both sides would leave you with 10/9 in fraction form
Answers
The figures that are scaled copies of the original figure A include the following: B. 2 and 4.
What is dilation?
A dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.
In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:
- A geometric figure is enlarged when the scale factor is greater than 1.
- A geometric figure remains the same when the scale factor is equal to 1.
- A geometric figure is reduced when the scale factor is less than 1.
In this context, we can logically deduce that the scaled copies of the original figure A are figure 2 and figure 4 because dilation preserves angle measures and the direction that the shape faces.
Read more on dilation here: brainly.com/question/11812796
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Complete Question:
Here is a figure that looks like the letter A, along with several other figures. Which figures are scaled copies of the original A?
2 and 3
2 and 4
1 and 4
1 and 3
Answer:
i think 2 and 4
Step-by-step explanation:
Answers
Answer:
y-8=1(x-4)
Step-by-step explanation:
I used the equations y-y/x-x and y-__y__=__m__(x-__x__)
Answers
Answer: -5g + 15h - 25 = -5 × (g - h + 5)
Step-by-step explanation:
Step-by-step explanation:
first we do this -5g = -5 × g
then 15h = 5 × 3h
so, -25 = -5 × 5
when -5g + 15h - 25 = -5 × g - (-5 × 3h) + (-5 × 5)
the answer is = -5 × (g - h + 5)
According to the Factors of a Negative Number
First The factors of a number entail all of the numbers that can be multiplied by one another to produce that many numbers.
According to The laws of multiplication that the state when a negative number is multiplied by a positive number then also the product will be negative.
Although when the Factors are those numbers. when it is multiplied with together then the result is another number, which is known as a product.
Answers
Now, all we need to do is convert the mixed fraction into an improper fraction:
Now, just multiply the reciprocal of 5/4 with 7/12, giving us:
Finally, just straight up multiply to get an answer of x = 28/60, which can be simplified down to x = 7/15. Therefore, the number you have to multiply 1 1/4 to get 7/12 is 7/15. Hope this helped!
Let x represent the number:
x . 5/4 = 7/12
i.e. 5x/4 = 7/12
We want to get x on it's own so multiply both sides of equation by 4
5x = 4 . (7/12) = 28/12
now divide both sides by 5 to get x on its own
x = (28/12) / 5
This does not equate to a whole number fraction as 28 and 12 are not divisible by 5. So simply convert to decimal
x = 2.3333 / 5 = 0.46666