# Bivariate Data Values

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Managers of an outdoor coffee stand in Coast City are examining 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 , in dollars) and the maximum temperature (denoted by , in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below.

Temperature, x Coffee sales, y

(in degrees Fahrenheit) (in dollars)

51.2 2246.1

75.4 1946.6

67.9 1734.1

74.5 1668.3

57.3 1945.5

46.4 2152.9

44.9 1778.5

56.2 1642.5

45.9 1979.3

65.0 1795.6

71.7 1951.4

53.8 1824.7

75.0 1524.6

39.1 2236.8

81.7 1547.0

38.5 1959.4

The least-squares regression line for these data has a slope of approximately . Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below.

1. 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.

2. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.

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##### Solution Summary

Managers of an outdoor coffee stand in Coast City are examining 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 , in dollars) and the maximum temperature (denoted by , in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below.

Temperature, x Coffee sales, y

(in degrees Fahrenheit) (in dollars)

51.2 2246.1

75.4 1946.6

67.9 1734.1

74.5 1668.3

57.3 1945.5

46.4 2152.9

44.9 1778.5

56.2 1642.5

45.9 1979.3

65.0 1795.6

71.7 1951.4

53.8 1824.7

75.0 1524.6

39.1 2236.8

81.7 1547.0

38.5 1959.4

The least-squares regression line for these data has a slope of approximately . Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below.

1. 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.

2. What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places

##### Solution Preview

Because,

<br><br><X> = 59.03

<br><br><Y> = 1870.83

<br><br>Sx^2 = Sum of Sq. of X - n*<X>^2 = 3001.03

<br><br>Sy^2 = ...

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- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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