Question

The director of sales at a large ice-cream parlor company want to see if there is a relationship between Ice-cream sales and temperature. They have 15 different parlors from all over the country report on their sales total for a day in the week and what the hi temperature temperature was that day. The data collected is given below. 1. What conclusion can be drawn 2. Predict the amount of money a parlor would make when the temp. reaches 85 Temp Sales 57 195 60 215 65 180 50 175 63 330 70 405 78 525 75 410 88 620 85 550 BD R3 430 445 90 550 93 700 I reall O

correlation and regression

Answer 1

Run a regression analysis in excel followed by below procedures: 1. Go to data tab --> data analysis --> choose Regression Regression ? х Input Input Y Range: OK $B$1:$B$16 1 с Cancel к Input X Range: $A$1:$A$16 Help Constant is Zero Labels Confidence Level: 95 96 Output options $E$3 1 A 1 Temp 2. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 B Sales 57 195 60 215 65 180 50 175 63 330 70 405 78 525 75 410 88 620 85 550 80 425 83 430 85 445 90 550 93 700 O Qutput Range: New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

Result: с D E F - G H J к L M N SUMMARY OUTPUT А B 1 Temp Sales 2 57 195 3 60 215 4 65 180 5 50 175 6 63 330 7 70 405 8 78 525 9 75 410 10 88 620 11 85 550 12 80 425 13 83 430 14 85 15 90 550 16 93 700 17 Regression Statistics Multiple R 0.926 R Square 0.857 Adjusted R Square 0.846 Standard Error 64.847 Observations 15 ANOVA df Significance F 0.0000008 445 1 Regression Residual Total SS MS F 326606.287 326606.3 77.66803 54667.04632 4205.157 381273.3333 13 14 18 Intercept Temp Coefficients Standard Error -451.826 99.251 11.526 1.308 t Stat -4.552 8.813 P-value 0.001 0.000 Lower 95% Upper 95%ower 95.0%pper 95.0% -666.245 -237.407 -666.245 -237.407 8.701 14.352 8.701 14.352 19 20 21 22 23 correlation coefficient (Multiple 1) = 0.926 Regression equation: y = -451.826 + 11.526x

Predict the temp when temp. reaches 85: x=85 y=-451.826 + 11.526*(85) = 528 when the temp is 85, the predicted sales is 528 P-value (Significance F) = 0.0000008 Conclusion: If the p-value is less than the significance level (a=0.05): Decision: Reject the null hypothesis. Conclusion: "There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero."