Please answer in an hour! Help Please!

Chiz-E-pizza, a family owned pizzeria, is famous not only for its innovative flavors, but also for delivering incredibly on time. However, during the last few weeks, the company has been facing an increase in customers complaints about late deliveries. Brian Flores, the owner, suspects that the problem is related to the GPS platform they are currently using to calculate the estimated delivery time that is informed to customers. "This is affecting customer's expectations and compromising our level of service", he says. Brenda, his tech loving daughter, replies: "The platform is probably underestimating some important factors that impact on traffic. Let me investigate this".

Brenda wants to investigate what factors could be impacting the difference from the Estimated Time of Arrival - ETA from the current GPS platform to the actual delivery time. "It's been raining more than usual during the last month", she says, "I am convinced that it impacts traffic, and I guess the platform does not take this rain factor into account". Therefore, she takes precipitation reports from the last 30 days in order to analyze if rain is somehow related to the daily average delays.

The following table includes information about daily average delay and precipitation for the last 30 days.

Day	Daily Average Delay (minutes)	Precipitation (in)
1	15	0.76
2	1.5	0.07
3	12	0.58
4	16.5	0.06
5	1.5	0
6	9	0.27
7	10.5	0.29
8	7.5	0.24
9	19.5	1.1
10	12	0.31
11	3	0
12	28.5	1.06
13	1.5	0.03
14	22.5	0.7
15	1.5	0.01
16	3	0
17	1.5	0.04
18	30	1.26
19	13.5	0.42
20	1.5	0
21	48	2.25
22	4.5	0.02
23	9	0
24	3	0.01
25	1.5	0.01
26	1.5	0
27	1.5	0
28	1.5	0.13
29	1.5	0
30	10.5	0.51

Create a linear regression model to verify Brenda's assumption, that is, if there is a relation between precipitation and delays.

What is the R²of this model?

What is the model's intercept value?

What is the model's slope value?

Question 2

Brian is impressed by his daughter's insight to associate the delays to the weather. However, he did not understand how her findings could be used to improve deliveries level of service. Brenda explains that, at the beginning of each day, they could take the forecasted precipitation volume for that day, and then use her equation to estimate an average delay for that day. With that, they could add the estimated average delay provided by her model to each of the ETAs provided by the GPS platform during that day. Then, they could inform a more accurate delivery time to each customer. "We can avoid frustrating customer's expectations by providing a more accurate ETA".

Based on the regression model, how much time (in minutes) should Chiz-E-pizza add to the ETA provided by the GPS platform in a day in which the forecasted precipitation volume is 1.15 inches?

"What if the forecast for a specific day is no precipitation? Or an extreme amount of precipitation, like 10 inches?", Brian asks. Considering Brian's question, and the model created with the dataset above, choose the correct option:

It is recommended to use this model only for the first option, that is, no precipitation.

It is recommended to use this model only for the second option, that is, 10 inches precipitation.

This model cannot be used in any of these two situations.

This model can confidently be used in both situations.

None of the above

Question 3

Brian liked Brenda's approach. They started to discuss what other factors could be somehow related to those delays. She remembered that two months ago the local government launched a parking restriction policy, on Tuesdays, Wednesdays and Thursdays. She suspects this may be causing difficulties for delivery drivers to park, and increasing delays in orders delivered during the parking restriction days. To investigate this hypothesis, Brenda decides to include Parking Restriction as an additional variable in her regression model.

The following table includes information about daily average delay, precipitation and day of the week, for the last 30 days.

Day	Daily Average Delay (minutes)	Precipitation (in)	Day of the week
1	15	0.76	Sunday
2	1.5	0.07	Monday
3	12	0.58	Tuesday
4	16.5	0.06	Wednesday
5	1.5	0	Thursday
6	9	0.27	Friday
7	10.5	0.29	Saturday
8	7.5	0.24	Sunday
9	19.5	1.1	Monday
10	12	0.31	Tuesday
11	3	0	Wednesday
12	28.5	1.06	Thursday
13	1.5	0.03	Friday
14	22.5	0.7	Saturday
15	1.5	0.01	Sunday
16	3	0	Monday
17	1.5	0.04	Tuesday
18	30	1.26	Wednesday
19	13.5	0.42	Thursday
20	1.5	0	Friday
21	48	2.25	Saturday
22	4.5	0.02	Sunday
23	9	0	Monday
24	3	0.01	Tuesday
25	1.5	0.01	Wednesday
26	1.5	0	Thursday
27	1.5	0	Friday
28	1.5	0.13	Saturday
29	1.5	0	Sunday
30	10.5	0.51	Monday

What is the R²of this model?

Based on the new regression model, how much time should Chiz-E-pizza add to the ETA provided by the GPS platform in a Friday in which the forecasted precipitation volume is 0.5 inches?

Question 4

Brian got really interested in linear regression models and started to study more about it. A few weeks later, his daughter came up with a test to check his knowledge.

Which of the following statements are true?

Linear regression models can have many independent variables, but only one dependent variable.

The error term, also known as residual, is the unexplained portion of a linear regression model.

It is not possible to create a model using both continuous and binary variables on it.

The adjusted R2 of a model will never be greater than the R2 of the model.

If the adjusted R2 of a model equals 0.5, this means that the model explains 50% of the variation of the dependent variable.

None of the above