A study was performed for an ice-cream shop located at a popular beach in the US
ID: 3376509 • Letter: A
Question
A study was performed for an ice-cream shop located at a popular beach in the USA. The store owner wanted to analyse the relationship between ice-cream weekly sales (in dollars) and the maximum weekly temperature (°F) at the beach. The values of both variables were recorded each day for one year. At the end of the year, a random sample of 21 weeks of ice-cream sales and maximum weekly temperatures was selected. A regression analysis was performed and the output from Excel is shown below. The maximum weekly temperatures in this sample ranged from 63 °F to 100 °F.
(a) State the estimated simple linear regression equation.
(b) Interpret the coefficient for maximum weekly temperature.
(c) Predict the weekly ice-cream sales (in dollars) when the maximum weekly temperature is 110 °F. Do you have any reservations about this prediction? Explain.
(d) Using ? = 5%, perform a test to determine whether there is a significant positive relationship between the maximum weekly temperature and weekly ice-cream sales. Use the p-value method.
Regression Statistics R Square Standard Error Observations 0.921 0.169 21 ANOVA df MS Regression Residual Total 6295886 6295886 19 20 542628 6838514 28559 Coefficients 2484 60 value Intercept Max, weekly Temperature 0.04 0.062Explanation / Answer
(a) simple linear regression equation.
ice-cream weekly sales (in dollars)=-2484+60 (maximum weekly temperature (°F) )
(b) Interpret the coefficient for maximum weekly temperature.
coefficient for maximum weekly temperature is 60 ( SLOPE).
The slope beta1 (60) is the change in the Mean of the the distribution of Y(ice-cream weekly sales (in dollars) ,when ther is a unit change in maximum weekly temperature(X).
(c) Predict the weekly ice-cream sales (in dollars) when the maximum weekly temperature is 110 °F.
ice-cream weekly sales (in dollars)=-2484+60 (110(°F) )
ice-cream weekly sales (in dollars)=4116
(d) Simple linear regression
ice-cream weekly sales (in dollars)=-2484+60 (maximum weekly temperature (°F) )... [1]
Above equation shows that positve sign of intercept So its positve relationship between response variable and regressor variable at 5% l.o.s.
R Square =0.921 shows that peffect positive relationshipe between ice-cream weekly sales (in dollars)(Y) and maximum weekly temperature (°F) .
P-values shows thats its coefficients is statistically sifgnificant.
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