A consumer buying cooperative tested the effective heating area of 20 different

Question

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the 0.010 significance level. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.)

Develop the regression equation for effective heating based on wattage. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

What is the regression equation?

Which heater looks like the “best buy” based on the size of the residual? (Round residual value to 2 decimal places.)

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

Explanation / Answer

20

A.  Number of cases 20
X = 24250
Y = 3159
X^2 = 33187500
Y^2 = 594055
XY = 4393750
X Y = 4393750

r = ( XY - X Y / n ) / SQRT { [ X^2 - (X)^2 / n] [ Y^2 - (Y)^2 / n]}
Numerator of r = (4393750) - (24250)(3159) / 20 = 563462.5
Denominator of r = SQRT[33187500 - (24250)^2 / 20] * SQRT[594055 - (3159)^2 / 20]
= SQRT[3784375] * SQRT[95090.95]
r = 563462.5 / [1945.34701] * [308.36821]
Correlation coefficient r = 0.939

Correlation coefficient is strongly positive and close to 1. This tels us that there is strong positive relationship between the two variables.

B.

So it is reasonable to conclude that the coefficient is greater than zero.

C.

Area = 0.1489(Wattage) - 22.581

D.

Regression Statistics Multiple R 0.939287066 R Square 0.882260193 Adjusted R Square 0.875719093 Standard Error 24.93991679 Observations

20

ANOVA df SS MS F Significance F Regression 1 83894.96 83894.96 134.8795 8.52964E-10 Residual 18 11195.99 621.99945 Total 19 95090.95 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -22.58133774 16.514681 -1.3673493 0.188349 -57.27739498 12.11472 -57.277395 12.11472 Wattage 0.148891825 0.0128203 11.613762 8.53E-10 0.121957391 0.1758263 0.12195739 0.1758263

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