(3) At the significance level α=0.05, use the t test method to test whether the volume of advertisements will affect sales, that is, test whether the slope of the linear relationship of the regression is 0. (5 points)

題組內容

1. An international business uses a simple linear regression model to establish the relationship between its sales (Y) and the volume of advertisements (X).

Given the following 10 sets of data (y1, x1),...(y10, x10), where yi is the sales in the ith month, and xi is the number of advertisements in the ith month. According to the information:

10 sales data y1,..., y10, the average value of yi is 130, and the variance is 1748. The number of advertisements for 10 advertisements is x1,...,x10, and the average value of xi is 14. In addition, the sales data y1,...,y10, and the advertisement frequency data x1,...,x10, the covariance is 316.

Using the least squares method, the estimated regression relationship is Y = 60 + 5X.

2. Assuming that there are 3 possible variants during a disease epidemic related to COVID-19: A, British variant, B, South African variant, and C, American variant of COVID-19 disease.Among them, the probability of infected patients is that the probability of the A British variant new coronary pneumonia disease is 0.6, the B South African variant new coronary pneumonia disease probability is 0.3, and the C American variant new coronary lung disease probability is 0.1.These three types of new coronary pneumonia diseases may have fever and cough symptoms. Among them, 20% of patients with A: British variant have fever, 60% of patients with B: South African variant have fever, and 80% of patients with C: American variant have fever; And 50% of patients with variant A in the UK have cough symptoms, 35% of patients with variant B in South Africa have cough symptoms, and 25% of patients with variant C in the United States have cough symptoms.An existing patient who is infected has fever symptoms. Please calculate the probability of this patient to have these three types of new coronary pneumonia, and determine which type of new coronary pneumonia the patient is most likely to have. (10 points)

題組內容

(3) At the significance level α=0.05, use the t test method to test whether the volume of advertisements will affect sales, that is, test whether the slope of the linear relationship of the regression is 0. (5 points)

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