The file "BCRperu" in Excel (data link) contains the credits of the banking companies to the private sector (in millions of soles) in Peru during 349 months between the years 1992-2021. The variables included in the file are: (1) the obligations (debts) of the private sector (Column B, in millions of soles), and (2) the cash in the private sector (Column C, in millions of soles). In order to study the relationship between obligations and cash in the private sector, please use the simple random sample of size ???? = 100, n=100 that was assigned to you for analysis.

Select the correct answer. All your calculations should be rounded to four decimal places. Using the data from the variable "obligations" make a histogram and the normality test (Shapiro's test) for these data.

Data link

Fecha","Obligaciones","Caja"

"Feb07",4806.42252,1359.827

"Feb20",25747.131,6318.843

"May07",6541.617805,1358.234

"Mar08",7859.194,1473.537

"Sep95",980.789,328.805

"Mar93",241.411,138.965

"Ene16",20189.695,5056.692

"May02",4077.852,569.17862142

"Jun04",3965.611,794.69

"Dic00",4039.531,718.85696644

"Ago04",4097.252,802.266

"Ago06",4905.374794,1214.257

"May92",91.137,94.945

"Ago11",11428.865,3234.108

"Ene99",4385.531,610.75696644

"Nov92",176.548,131.237

"Jul99",4870.131,753.25696644

"Sep08",8376.624,1939.327

"Jul03",3772.342,752.069

"Mar04",3933.147,697.361

"Ene01",4002.674,678.39105912

"Sep02",3943.052,594.47862142

"Jun96",1269.331,402.45696644

"Dic12",14400.486,4094.382

"Ago92",109.566,97.966

"Abr09",8986.906,1971.094

"Jul94",561.193,228.684

"Sep07",7385.577466,1424.04

"Nov06",5122.107,1233.113

"Sep94",445.003,190.487

"May05",3985.724,853.074

"Sep04",4050.74,737.179

"Feb06",4174.175013,1077.534

"Jun14",17029.80548127,4824.145

"Jun15",18596.676,5620.384

"Jul16",19419.084,5564.112

"Ene20",23230.705,6541.472

"Nov07",7686.92333,1442.384

"Dic15",19354.355,5906.363

"Abr06",4144.57894,1097.026

"Ago95",911.599,372.618

"Abr92",92.515,93.418

"Feb98",2919.931,564.85696644

"Jul09",8885.84,2302.013

"Dic13",16485.662,5906.282

"Jun98",3218.831,669.75696644

"Jun19",24964.809,6096.381

"Jul97",2455.331,613.75696644

"Ago13",15997.256,4529.699

"Jun00",4510.631,636.45696644

"Sep10",10167.933,2331.363

"Mar98",2817.931,586.15696644

"Mar17",21223.061,5518.419

"May08",7937.259,1617.316

"Nov01",4113.274,596.19105912

"Sep92",145.192,123.044

"Nov18",24179.167,6013.009

"Jun06",4334.370775,1175.783

"Ene07",4732.200249,1377.484

"Dic97",2797.131,622.9

"Ene12",11336.342,3274.984

"May94",580.502,197.864

"Mar14",16894.254,4745.16

"Jun20",26954.17151086,6895.775

"Oct93",407.406,149.044

"Oct01",4093.174,652.59105912

"Jun05",3917.676,912.255

"Nov93",365.974,176.817

"Feb99",4366.131,650.35696644

"Ago93",445.428,191.033

"Feb13",14989.117,4100.585

"Nov15",19710.584,5286.352

"Feb19",27263.456,6409.328

"May17",21318.743,5451.029

"Feb08",7541.721,1525.565

"Ago01",4305.874,632.79105912

"May20",22621.7549561,6718.711

"Jul92",82.249,112.587

"Dic05",3595.215,1040.112

"Ene93",191.768,103.416

"Ene97",1937.931,507.25696644

"Mar96",1242.431,401.75696644

"Ago07",7277.552866,1470.272

"Jul05",3833.666,1044.965

"Ago19",24757.145,6457.146

"Jun10",9684.116,2457.36

"Jun99",4810.731,717.05696644

"Feb11",9409.174,2537.641

"Ene98",2794.831,536.55696644

"Nov11",11625.991,3136.909

"Mar09",9460.774,2062.249

"Dic03",3684.877,717.161

"Ene14",17920.57,4937.107

"Feb00",4653.131,654.35696644

"Ago10",9692.841,2273.951

"Abr02",3947.352,598.37862142

"Jul14",16458.23390789,5751.485

"Jun12",13438.243,3406.619

"Oct94",582.309,213.692

"Oct00",4238.231,617.95696644

Question 1: The histogram has a distribution:

Asymmetric to the left (shifted to the left)

Asymmetric to the right (shifted to the right)

Symmetric, there is normality in the data

Symmetric but there is no normality

Question 2: In Shapiro's test, the p value was:

Answer _____ (use four decimal places).

Question 3: According to Shapiro's test it is inferred that:

Interpreting the Shapiro test result: There is no evidence of normality in the data

Interpreting the result of Shapiro's test: There is normality in the data.

Question 4: Make the scatter diagram of the variables box and obligations, where box is the explanatory variable (independent) and obligations the response variable (dependent).

The graph shows that: there is a positive linear relationship between the two variables there is a negative linear relationship between the two variables

There is no linear relationship between the two variables

Question 5: The value of the correlation coefficient is: Answer _____ (use four decimal places)

Question 6: From the scatter plot and correlation, we can say that

a. There is a weak positive linear relationship between the two variables

b. There is a weak negative linear relationship between the two variables

c. There is a strong positive linear relationship between the two variables

d. There is a strong negative linear relationship between the two variables

e. None of the other options

The theoretical model of Simple Linear Regression of the response variable (dependent) as a function of the explanatory variable (independent) is presented below.

Identify each term.

????=????0+????1????+????

The variable Y refers to:

a. intercept

b. obligations

c. box

d. regression coefficient (slope) and. error

. The variable X refers to:

a. intercept

b. obligations

c. box

d. regression coefficient (slope)

e. error

.The parameter 0 refers to:

a. intercept

b. obligations

c. box

d. regression coefficient (slope)

e. error

.Parameter 1 refers to:

a. intercept

b. obligations

c. box

d. regression coefficient (slope)

e. error

The term E refers to:

a. intercept

b. obligations

c. box

d. regression coefficient (slope)

e. error

Find the estimated regression line, considering the simple linear regression model.

Question 8: The estimated value of the intercept is: Answer ___ (use four decimal places)

Question 9: The estimated value of the regression coefficient (slope) is: Answer ___ (use four decimal places)

Find the ANOVA table of the regression analysis. Using the table, answer the following questions. Round to four decimal places.

Question 10: The alternate hypothesis in this analysis is:

a. The cash variable has a linear influence on the obligations variable

b. The cash variable does not have a linear influence on the obligations variable

c. The cash variable is very close to the obligations variable

d. The cash variable is very far from the obligations variable

Question 11: The value of the test statistic, F, is equal to: Answer (use four decimal places).

Question 12: The value of the p value is: Answer use four decimal places)

Question 13: Interpretation: When the cash is increased by 10 million soles in the private sector, what happens to the value of the obligations? Use the estimated regression coefficient to answer the question.

a. Increase decreases 35,347 million soles.

b. Increases by 35,347 million soles

c. Decreases by 8522.301 million soles

d. Increases by 8522.301 million soles

Question14: The value of the coefficient of determination is: Answer (use four decimal places)

Question 15: Interpretation of the coefficient of determination is: Answer

a. At least 90% of the variability of obligations is explained by the estimated regression model

b. Less than 90% but at least 75% of the variability of obligations is explained by the regression model

c. Less than 75% but 50% or more of the variability of obligations is explained by the estimated regression model.

d. Less than 50% of the variability of obligations is explained by the estimated regression model

Question 16: Find the forecast (prediction) of the obligations of a company that has 4845 million soles in cash. Find the prediction interval of 90% confidence.

The forecast value of the obligations in millions of soles is: Answer (use four decimal places)

Question 17: The limits of the 90% confidence prediction interval are:

a.The lower limit is: Answer (use four decimal places)

b. The upper limit is: Answer (use four decimal places)

Question 18: Make the appropriate graphs to evaluate the assumptions of the model errors:

(1) uncorrelated, (2) Normally distributed, and (3) homogeneity of variance. What do the graphs suggest?

About uncorrelated errors (error independence):

a. Errors are not correlated for fitted model

b. There is no evidence to assume that the errors are correlated for the fitted model

On the normality of errors: (delete as it is asked with Shapiro) Answer

a.Suppose normality of the waste

b. There is no evidence to assume normality of the residuals

On the homogeneity of variance of the errors:

a. We assume homogeneity of variances

b. There is no evidence of homogeneity of variances