Concept explainers
A
Interpretation:Based on the expected average air temperature, estimate the next month sales using the linear regression model.
Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to
A
Answer to Problem 28P
After necessary calculations, we can observe that the slope value is -1.626.
Explanation of Solution
Given Information:
The number of months is 42, n.
Multiplied value of average temperature and average sales is 873,931,∑xy.
Sum of squared monthly temperature is 105,080,∑x2.
Sum of air temperature reading is 2,058,∑x.
Sum of sales is 17,976,∑y.
Now, we will derive intercept,
Thus, the value of intercept is 507.64.
Now, substitute these values in the below equation,
This means, the approximate value is 451 rolls insulation.
B
Interpretation:Determine the percent of variation in the sales in the past 42 months, by observing the linear relationship to the average temperature.
Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.
B
Answer to Problem 28P
After necessary calculations, we can observe that the percent of variation is 68.56%.
Explanation of Solution
Given Information:
Number of months, n is 42 months.
Multiplied value of average temperature and average sales,∑xy is 873,931.
Sum of squared monthly temperature,∑x2 is 105,080.
Sum of air temperature reading,∑x is 2058.
Sum of sales,∑y is 17976.
Sum of squared monthly sales,∑y2 is 7710080.
49 degrees of average air temperature, x-.
428 rolls of average sales, y-.
First, let us find out correlation coefficient,
Now, we shall determine the percentage of variation.
C
Interpretation: Determine the correlation coefficient between sales and average air temperature, and also briefly put out the relationship between those two.
Concept Introduction: Using regression, we will be able to define relationship between any two variables, denoting the cause and effect. The method can also be used to forecast the future depending on the past performances.
C
Answer to Problem 28P
The correlation coefficient is -0.828, and this indicates that the sales will increase with a decrease in the air temperature.
Explanation of Solution
Given Information:
Number of months, n is 42 months.
Multiplied value of average temperature and average sales,∑xy is 873,931.
Sum of squared monthly temperature,∑x2 is 105,080.
Sum of air temperature reading,∑x is 2058.
Sum of sales,∑y is 17976.
Sum of squared monthly sales,∑y2 is 7710080.
49 degrees of average air temperature, x-.
428 rolls of average sales, y-.
Thus, we can see that there will be an increase in the sales with a decrease in the air temperature.
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Chapter 4 Solutions
Practical Operations Management
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