Use the Regression tool on the accompanying wedding data, using the wedding cost as the dependent variable and attendance as the independent variable. Complete parts a through c.

Wedding Cost | Attendance
--- | ---
58700 | 300
50000 | 350
47000 | 150
44000 | 200
35000 | 250
31500 | 150
31000 | 250
29000 | 300
28000 | 250
27000 | 200
27000 | 150
24000 | 200
22000 | 200
22000 | 200
21000 | 200
20000 | 200
19000 | 100
19000 | 150
18000 | 200
17000 | 150
15000 | 100
15000 | 100
14000 | 150
6000 | 50
4000 | 50

a. What is the regression model?
\[ \text{Wedding Cost} = \_\_\_\_\_ + \_\_\_\_\_ \times \text{Attendance} \]
(Round to three decimal places as needed.)

b. Interpret all key regression results, hypothesis tests, and confidence intervals in the regression output from part a.
- Interpret the slope of the regression equation. Choose the correct answer below:
A. The slope indicates that for each increase of 1 in wedding cost, the predicted attendance is estimated to increase by a value equal to $ b_1 $.
B. The slope indicates that for each increase of 1 in attendance, the predicted wedding cost is estimated to increase by a value equal to $ b_1 $.
C. It is not appropriate to interpret the slope because it is outside the range of observed wedding costs.
D. It is not appropriate to interpret the slope because it is outside the range of observed attendances.

- Interpret the Y-intercept of the regression equation. Choose the correct answer below:
A. The Y-intercept indicates that a wedding with a cost of $0 has a mean predicted attendance of $ b_0 $ people.
B. It is not appropriate to interpret the Y-intercept because it is outside the range of observed wedding costs.
C. It is not appropriate to interpret the Y-intercept because it is outside the range of observed attendances.
D. The Y-intercept indicates that a wedding with an attendance of 0 people has a mean predicted cost of $ \$b_0 $.

- Identify and interpret the meaning of the coefficient of determination in this problem. Select the correct choice below and fill in the answer box to complete your choice.
(Round to three decimal places as needed.)
A. The coefficient of determination is $ R^2 $ ___. This value is the probability that the correlation between the variables is statistically significant.
B. The coefficient of determination is $ R^2 $ _. This value is the proportion of variation in attendance that is explained by the variation in wedding cost.
C. The coefficient of determination is $ R^2 $ _. This value is the probability that the slope of the regression line is statistically significant.
D. The coefficient of determination is $ R^2 $ ___. This value is the proportion of variation in wedding cost that is explained by the variation in attendance.

- Interpret the values given in the test of the population slope. Use $\alpha = 0.05$ level of significance. State the null and alternative hypotheses for the test.
$ H_0 $: _________
$ H_1 $: ___
(Round to two decimal places as needed.)

- Identify the p-value.
The p-value is _
(Round to three decimal places as needed.)

- State the conclusion.
- Fail to reject
- Reject
$ H_0 $.
There is _______
- sufficient
- not sufficient
evidence of a linear relationship between wedding cost and attendance.

- Identify and interpret the 95% confidence interval estimate of the population slope.
The confidence interval is $ \_\_\_\_ \leq $
- $ b_0 $
- $ \beta_1 $
- $ b_1 $
- $ \beta_0 $
$ \leq \_\_\_\_. $ With 95% confidence, it can be said that the true expected mean increase in
- wedding cost
- attendance
per additional
- person attending
- dollar spent on
the wedding is within the bounds of the confidence interval.
(Round to three decimal places as needed.)

c. If a couple is planning a wedding for 325 guests, how much should they budget?
They should budget \$___________
(Round to the nearest dollar as needed.)

The 95% confidence interval cestimate of the population slope is obtained from the regression output and provides a range of values within which we can be 95% confident that the true population slope falls.

Here, we have,

a. The regression model is:

Wedding Cost = b₀ + b₁ * Attendance

b. The interpretation of the slope of the regression equation is:

D. The slope indicates that for each increase of 1 in wedding cost, the predicted attendance is estimated to increase by a value equal to b1.

c. The interpretation of the Y-intercept of the regression equation is:

B. The Y-intercept indicates that a wedding with an attendance of 0 people has a mean predicted cost of $b0.

The coefficient of determination (R²) in this problem represents the proportion of variation in wedding cost that is explained by the variation in attendance.

Therefore, the correct interpretation is:

B. The coefficient of determination is R² = [value]. This value is the proportion of variation in wedding cost that is explained by the variation in attendance.

The null and alternative hypotheses for the test of the population slope are:

H₀: The population slope (b₁) is equal to 0.

H₁: The population slope (b₁) is not equal to 0.

The test statistic used to test the population slope is t-test.

The conclusion of the test should be based on the p-value obtained from the test. If the p-value is less than the significance level (0.05), we reject the null hypothesis and conclude that there is evidence of a linear relationship between wedding cost and attendance.

The 95% confidence interval estimate of the population slope is obtained from the regression output and provides a range of values within which we can be 95% confident that the true population slope falls.

To determine the budget for a wedding with 325 guests, we can use the regression model and substitute the value of attendance into the equation to get the predicted wedding cost.

Learn more about regression model here:

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