Questions: The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The accompanying data table gives the value and the annual revenue for 15 major sport teams. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Complete parts (a) through (e) below, Click the icon to view the table of franchise values and annual revenues. b0=-300.98 b1=3.33 (Round to two decimal places as needed.) c. Interpret the meaning of b0 and b1 in this problem. Choose the correct answer below. A. The Y -intercept, b0, implies that if the annual revenue is zero, the franchise value is equal to the value of b0, in millions of dollars. The slope, b1, implies that the average franchise value is equal to b1, in millions of dollars. B. An interpretation of the Y-intercept, b0, is not meaningful because no sports franchise is going to have a revenue of zero. The slope, b1, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to increase by b1, in millions of dollars. c. The Y-intercept, b0, implies when the annual revenue is zero, the franchise value is b0, in millions dollars. The slope, b1. implies the revenue is equal to b1, in millions of dollars. D. The Y -intercept, b0, implies that if the annual revenue is zero, the franchise value is equal b0, in millions of dollars. The slope, b1, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to decrease by b1, in millions of dollars. d. Predict the mean franchise value (in millions of dollars) of a sports team that generates 200 million of annual revenue. Y^=s million (Round to the nearest integer as needed.)

The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The accompanying data table gives the value and the annual revenue for 15 major sport teams. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Complete parts (a) through (e) below,

Click the icon to view the table of franchise values and annual revenues.

b0=-300.98
b1=3.33

(Round to two decimal places as needed.)

c. Interpret the meaning of b0 and b1 in this problem. Choose the correct answer below.

A. The Y -intercept, b0, implies that if the annual revenue is zero, the franchise value is equal to the value of b0, in millions of dollars. The slope, b1, implies that the average franchise value is equal to b1, in millions of dollars.

B. An interpretation of the Y-intercept, b0, is not meaningful because no sports franchise is going to have a revenue of zero. The slope, b1, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to increase by b1, in millions of dollars.

c. The Y-intercept, b0, implies when the annual revenue is zero, the franchise value is b0, in millions dollars. The slope, b1. implies the revenue is equal to b1, in millions of dollars.

D. The Y -intercept, b0, implies that if the annual revenue is zero, the franchise value is equal b0, in millions of dollars. The slope, b1, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to decrease by b1, in millions of dollars.

d. Predict the mean franchise value (in millions of dollars) of a sports team that generates 200 million of annual revenue.

Y^=s  million (Round to the nearest integer as needed.)
Transcript text: The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The accompanying data table gives the value and the annual revenue for 15 major sport teams. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Complete parts (a) through (e) below, Click the icon to view the table of franchise values and annual revenues. \[ \begin{array}{l} \mathrm{b}_{0}=-300.98 \\ \mathrm{~b}_{1}=3.33 \end{array} \] (Round to two decimal places as needed.) c. Interpret the meaning of $\mathrm{b}_{0}$ and $\mathrm{b}_{1}$ in this problem. Choose the correct answer below. A. The Y -intercept, $\mathrm{b}_{0}$, implies that if the annual revenue is zero, the franchise value is equal to the value of $\mathrm{b}_{0}$, in millions of dollars. The slope, $\mathrm{b}_{1}$, implies that the average franchise value is equal to $\mathrm{b}_{1}$, in millions of dollars. B. An interpretation of the $Y$-intercept, $b_{0}$, is not meaningful because no sports franchise is going to have a revenue of zero. The slope, $\mathrm{b}_{1}$, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to increase by $\mathrm{b}_{1}$, in millions of dollars. c. Whe $Y$-intercept, $b_{0}$, implies when the annual revenue is zero, the frahchise value is $b_{0}$, in millions dollars. The slope, $b_{1}$. implies the revenue is equal to $\mathrm{b}_{1}$, in millions of dollars. D. The Y -intercept, $\mathrm{b}_{0}$, implies that if the annual revenue is zero, the franchise value is equal $\mathrm{b}_{0}$, in millions of dollars. The slope, $\mathrm{b}_{1}$, implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to decrease by $\mathrm{b}_{1}$, in mitlions of dollars. d. Predict the mean franchise value (in millions of dollars) of a sports team that generates $\$ 200$ million of annual revenue. $\hat{\mathrm{Y}}=\mathrm{s}$ $\square$ million (Round to the nearest integer as needed.)
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Solution

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Solution Steps

Step 1: Interpret the meaning of \( b_0 \) and \( b_1 \)

The question asks for the interpretation of the Y-intercept (\( b_0 \)) and the slope (\( b_1 \)) in the context of the linear regression model. The correct interpretation is:

  • Y-intercept (\( b_0 \)): This represents the predicted franchise value (in millions of dollars) when the annual revenue is zero. However, in this context, it is not meaningful because no sports franchise would have zero revenue.
  • Slope (\( b_1 \)): This represents the change in franchise value (in millions of dollars) for each increase of 1 million dollars in annual revenue.

The correct answer is B:

  • An interpretation of the Y-intercept, \( b_0 \), is not meaningful because no sports franchise is going to have a revenue of zero. The slope, \( b_1 \), implies that for each increase of 1 million dollars in annual revenue, the franchise value is expected to increase by \( b_1 \), in millions of dollars.
Step 2: Predict the mean franchise value for a given annual revenue

The linear regression model is given by: \[ \hat{Y} = b_0 + b_1 X \] where:

  • \( \hat{Y} \) is the predicted franchise value (in millions of dollars),
  • \( X \) is the annual revenue (in millions of dollars),
  • \( b_0 = -300.98 \),
  • \( b_1 = 3.33 \).

For \( X = 200 \) million dollars, the predicted franchise value is: \[ \hat{Y} = -300.98 + 3.33 \times 200 \] \[ \hat{Y} = -300.98 + 666 \] \[ \hat{Y} = 365.02 \] Rounding to the nearest integer: \[ \hat{Y} = 365 \]

Final Answer

  • Interpretation of \( b_0 \) and \( b_1 \): The answer is B.
  • Predicted franchise value for \$200 million annual revenue: \(\boxed{365}\) million dollars.
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