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The table shows ticket sales during the first week. Write an equation of the regression line. Then estimate the daily ticket sales on the 15th day after the movie opens.

Days Since Movie Opened

1

2

3

4

5

6

7

Daily Ticket Sales ($)

85

92

89

78

65

68

55

Short Answer

Expert verified

The required equation of the regression line is: y=5.79x+99.14. The ticket sales on 15th day after the movie opened is $12.29.

Step by step solution

01

Step 1. Rearrange the table.

Let

X-axis = days since movie opened.

localid="1647414443286" Y-axis = daily ticket sales (localid="1647414438033" $).

Using the regression calculator to find the equation of the regression line:

Days since sale began (localid="1647414432810" x)

Daily Sales (localid="1647414423922" y)

1

85

2

92

3

89

4

78

5

65

6

68

7

55

02

Step 2. Find the regression equation.

SumofX=28SumofY=532MeanX=4MeanY=76Sumofsquares(SSX)=28Sumofproducts(SP)=162

Regression Equation: ŷ=bX+a

b=SP/SSX=162/28=5.78571a=MYbMX=76(5.79×4)=99.14286=5.78571X+99.14286

03

Step 3. Plot the graph.

Graph the line y^=5.79X+99.14with slope aand intercept b.

Thus, the regression equation is y^=5.79X+99.14.

04

Step 4. Put the value of X to find the estimated sales.

Substituting the value of x=10in regression equation to find the daily sales on day 10 of the sale :

y^=5.79X+99.14y^=5.79(15)+99.14y^=86.85+99.14y^=12.29

So, The ticket sales on 15th day after the movie opened = $12.29.

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