Managers of an outdoor coffee stand in Coast City are examing the relationship b

Question

Managers of an outdoor coffee stand in Coast City are examing the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of fifteern randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1 Temperature, x (in degrees Fahrenheit) 51.7 55.3 40.7 45.4 71.9 38.3 81.9 66.8 47.2 76.7 60.0 75.4 70.3 48.2 62.1 Coffee sales, y (in dollars) 2236.6 1621.1 2273.9 1782.2 1650.7 2013.8 1568.5 1750.9 2139.0 1998.4 1948.2 1517.2 1987.3 1994.6 1822.5 40 50 0 70 0 90 Figure 1 The least-squares regression line for these data has a slope of approximately 10.40 Answer the following Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary consult a list of formulas.) What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places. Clear Undo Help

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 2505.0948 - 10.395248 x
Sample size: 15
R (correlation coefficient) = -0.61312862
R-sq = 0.37592671
Estimate of error standard deviation: 194.45691

Parameter estimates:

Analysis of variance table for regression model:

Hence,

y - intercept = 2505.09

Correlation coefficient = - 0.613

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 2505.0948 226.51359 0 13 11.059358 <0.0001 Slope -10.395248 3.7147484 0 13 -2.7983721 0.0151

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