Temperatures Ice Cream Sales 58 215 62 325 52 185 60 332 66 406 74 522 68 412 80

Question

Temperatures Ice Cream Sales 58 215 62 325 52 185 60 332 66 406 74 522 68 412 80 614 76 544 74 445 64 408 From the data above: -Calculate the correlation coefficient -Regression line and equation -Use the regression equation to compare an actual y versus a predicted y. Pick a point in your actual data (try and choose one that does not repeat). The y value of this point is the actualy. Next take the x value from that point and plug it into the regesssion equation equation to see what the line predicts they y will be. -What does the correlation coefficient tell you? Is it negative or positive? What does that mean related to your variables? Do you see a trend in the data? What does the coefficient of determination tell you Compare the real (actual y) from the data to the output the line gives. Write a brief paragraph explaigning your conclusions.

Explanation / Answer

The regression equation is y=a+bx

From Excel

a) From the above analysis

The correlation coefficient is 0.97

b) The regression equation is

y=14.86(x)-591.1

c) Residuals

d) From Excel The correlation coefficient is 0.97

Hence we conclude that there is a positive correlation between x and y

SUMMARY OUTPUT Regression Statistics Multiple R 0.967086 R Square 0.935256 Adjusted R Square 0.928062 Standard Error 35.41805 Observations 11 ANOVA df SS MS F Significance F Regression 1 163088.2 163088.2 130.009 1.19E-06 Residual 9 11289.94 1254.438 Total 10 174378.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -591.093 87.63845 -6.74468 8.42E-05 -789.345 -392.841 -789.345 -392.841 Temp 14.86379 1.303596 11.40215 1.19E-06 11.91485 17.81273 11.91485 17.81273

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