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A retail store wishes to predict their sales volume per week based on the number of minutes of commercial air time on television. The data is displayed below.
Minutes (x) 20 21 22 23 24 26 28 29 30 31 32 33 34 35
Sales (Thousands)(y) 63.3 65 69.1 70.1 70.9 69.4 76 82.6 73.3 73.8 94.1 92.4 98.2 96.1
The equation of the best fit line is (y hat) y^ =2.147x+ 18.6606

A residual is the distance between the observed y-value from the scatter plot and the predicted y-value from the equation- (y-hat) y^2.174x+18.6606
a. Find the observed y-value when x is 32
b. Find the predicted y-value when x is 32
c. Find the residual for this point



Answer :

semsee45

Answer:

a) y = 94.1

b) y = 87.3646

c) 6.7354

Step-by-step explanation:

Part a

The observed y-value refers to the actual value of the dependent variable (y) obtained from the provided data. Therefore, to find the observed y-value when x is 32, we simply find the corresponding y-value from the given table, which is y = 94.1.

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Part b

The predicted y-value is the value calculated using the line of best fit equation. Therefore, to find the predicted y-value when x is 32, substitute x = 32 into the equation:

[tex]y =2.147(32) + 18.6606\\\\y =68.704 + 18.6606\\\\y =87.3646[/tex]

Therefore, the predicted y-value when x is 32 is y = 87.3646.

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Part c

A residual is the difference between the observed y-value and the predicted y-value for a given independent variable. Therefore, to find the residual for this point, subtract the predicted y-value from the observed y-value:

[tex]\textsf{Residual}=94.1- 87.3646\\\\\textsf{Residual}=6.7354[/tex]

Therefore, the residual for this point is 6.7354.

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