Does anyone know the answer to this problem?

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graciouschea1 graciouschea1

21-06-2022
Mathematics

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Does anyone know the answer to this problem?

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MrRoyal MrRoyal · Answer 1 · 2022-06-21T22:23:15+02:00

The regression equation is y = 16.585x - 639.769 and the linear correlation coefficient indicates a strong linear relationship

How to determine the regression equation?

To do this, we make use of a statistical calculator;

Using the statistical calculator, we have the following summary:

Sum of X = 554
Sum of Y = 4070
Mean X = 69.25
Mean Y = 508.75
Sum of squares (SSX) = 725.5
Sum of products (SP) = 12032.5
Correlation coefficient, r = 0.9768

The regression equation is

ŷ = bx + a

Where:

b = SP/SSX = 12032.5/725.5 = 16.58511

a = MY - bMX = 508.75 - (16.59*69.25) = -639.76912

Hence, the regression equation is y = 16.585x - 639.769

The number of cans sold at 90 degrees F

This means that"

x = 90

So, we have:

y = 16.585 * 90 - 639.769

Evaluate

y = 852.881

Approximate

y = 853

Hence, 853 cans were sold at 90 degrees F

The linear correlation coefficient

In (a), we have:

r = 0.9768

This means that the linear correlation coefficient is 0.9768

The conclusion

We have:

r = 0.9768

The above value is closer to 1 because

|r| > 0.9

i.e.

0.9768 > 0.9

Hence, the linear correlation coefficient indicates a strong linear relationship