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Zanzabum
3 years ago
6

The similarities and differences between correlation and regression Correlation and regression are two closely related topics in

statistics. For each of the following statements, indicate whether the statement is true of correlation, true of regression, true of both correlation and regression, or true of neither correlation nor regression. Regression Correlation Both Correlation and Regression Neither Correlation nor Regression Can tell you whether one variable (such as smoking) causes another (such as cancer) Can be influenced by extreme values on one or both variables Can tell you the degree to which a linear relationship exists between two variables?
Mathematics
1 answer:
Anna [14]3 years ago
4 0

Answer:

Both variables Can tell you the degree to which a linear relationship exists between two variables.

Step-by-step explanation:

Correlation and regression are two statistical concepts that are closely related and complement each other. They are powerful tools used in modern-day machine learning and artificial intelligence.

Correlation evaluates the linear relationship between two variables, using regression as a tool to assess the degree at which a dependant variable changes ( either increasing or decreasing ) based on the value of an independent variable.

The correlation coefficient is the degree of the linear relationship between two variables, ranging from zero ( for non-linear) to one ( for highly linear).

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Use a t-distribution to find a confidence interval for the difference in means μd=μ1-μ2 using the relevant sample results from p
V125BC [204]

Answer:

a)

best estimate = Xd[bar]=4.80

margin of error = 8.66

The 99% confidence interval is -3.86 to 13.46

b)

test statistic = -1.86

p-value = 0.0526

Decision: Reject the null hypothesis.

At the 5% significance level, you can conclude that the population mean of the difference between treatment 1 and treatment 2 is less than zero.

Step-by-step explanation:

Hello!

a) 99% CI

Using d=X₁-X₂ to determine the study variable Xd: the difference between treatment 1 and treatment 2.

Assuming that this variable has an approximately normal distribution: Xd≈N(μd;σ²d)

To calculate the sample mean and standard deviation you have to calculate the difference between the values of both treatments first.

Case 1 ; Case 2 ; Case 3 ; Case 4 ; Case 5

22-18= 4 ; 27-29= -2 ; 32-25= 7; 26-20= 6 ; 29-20= 9

n= 5

Xd[bar]= ∑X/n= 24/5= 4.80

Sd²= 1/(n-1)*[∑X²-(∑X)²/n]= 1/4*[186-(24²)/5]= 17.7

Sd= 4.21

The parameter of interes is the population mean od the difference, μd

The best estimate for this parameter is the sample mean, Xd[bar]=4.80

Using the t-distribution, the formula for the Confidence Interval is

Xd[bar] ± t_{n-1;1-\alpha /2}*\frac{Sd}{\sqrt{n} }

Where the margin of error is:

t_{n-1;1-\alpha /2}*\frac{Sd}{\sqrt{n} }= t_{4;0.995}*\frac{Sd}{\sqrt{n} }= 4.604*\frac{4.21}{\sqrt{5} }= 8.66

99% CI [-3.86; 13.46]

b) 5% Hypothesis test

The variable of interest is defined d=X₁-X₂; Xd: the difference between treatment 1 and treatment 2. Xd≈N(μd;σ²d)

The statistic hypotheses are:

H₀: μd = 0

H₁: μd < 0

α: 0.05

The statistic to use for this test is:

t_{H_0}= \frac{X_d[bar]-Mu_d}{\frac{Sd}{\sqrt{n} } } ~~t_{n-1}

As before you have to calculate the difference between the observation for each case and then the sample mean and standard deviation:

Case 1  ; Case 2   ; Case 3   ; Case 4  ; Case 5  ; Case 6 ; Case 7  ; Case 8

18-18= 0; 12-19= -7; 11-25= -14; 21-21= 0; 15-19= -4; 11-14=-3; 14-15= -1; 22-20= 2

n= 8

Xd[bar]= ∑X/n= -27/8= -3.38

Sd²= 1/(n-1)*[∑X²-(∑X)²/n]= 1/7*[275-(-27²)/8]= 26.27

Sd= 5.13

t_{H_0}= \frac{-3.38-0}{\frac{5.13}{\sqrt{8} } }= -1.86

This test is one-tailed to the left, which means that you will reject the null hypothesis to small values of t, the p-value of the test has the same direction as the rejection region, this means that it is one-tailed to the left and you can calculate it as:

P(≤-1.86)= 0.0526

The decision rule using the p-value is:

If p-value > α, do not reject the null hypothesis.

If p-value ≤ α, reject the null hypothesis.

The p-value is greater than the significance level so the decision is to reject the null hypothesis.

I hope it helps!

7 0
4 years ago
Why are all of you getting answers from students, you know you guys are cheating
jeyben [28]

Answer:

it's not cheating, it's helping out fellow students and explaining it to them.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What are the x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 5:8? Round t
Fantom [35]

Answer:

(1.2, –4.7)

Step-by-step explanation:

Since in the question it is mentioned that on the plane of coordinate, a line is made from point A (7,-2) to point B(-8,-9)

Also, the ratio of A to B is 5:8

Based on this, the x and y coordinates at point C is

= [\frac{5\times (-8) + 8\times 7}{5 + 8} , \frac{5\times (-9) + 8\times -2}{5 + 8}]\\\\= [\frac{16}{3}, \frac{-61}{13}]

= (1.2, –4.7)

Hence, the x and y coordinates of point C is (1.2, –4.7)

Therefore the last option is correct

4 0
3 years ago
I need helppppppppppppp
Fantom [35]

Answer:$140 for the train ride

$84 for the museum

Step-by-step explanation:

28×5

28×3

All the students + you = 28

If not, try 27×5 and 27×3

3 0
3 years ago
Read 2 more answers
If two figures have equal area, the two figures will be congruent?​
galben [10]

Answer:

yes

Step-by-step explanation:

6 0
3 years ago
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