1. [Marks:16] Linear Regression: The research team of a 'Packers and Movers' company wants to fit a mul regression model to calculate appropriate delivery cost (Y, in Rs. in Thous consignment based on independent factors like distance (X1, in kms) between p and destination, number of boxes and furniture to be delivered (X2), and total va in Rs. in Lakhs) of items declared by customer. In order to achieve this, they c sample data on previous 520 consignments. The excel outputs for this regression given in Tables 1 - 3. Table 1. Coefficients Standard Error t Stat P-value Intercept 1.957141696 1.15890634 1.68878332 0.091865112 [X 0.039356022 0.000720116 54.65232193 9.5915E-217 X2 0.187450471 0.036999868 5.066247046 5.65992E-07 X3 0.194058707 0.062329411 3.113437188 0.001951846 Table 2. ANOVA df SS MS F Significance F Regression 3 a 15773.08 1013.163 9.049E-216 Residual 516 8033.17 b Total 519 55352.41 Table 3. Regression Statistics Multiple R 0.924593025 R Square 0.854872262 Adjusted R Square 0.854028496 Standard Error 3.945650551 Observations 520 Based on the outputs given in Tables 1 -3, please answer the following questions: a) Write down the complete fitted multiple linear regression equation. [2]b) For a new consignment, with distance between the pick-up point and destination being 1000 kms, 25 boxes to be delivered, and Rs. 5 lakh declared valuation of the items to be sent, what would be the predicted delivery cost? [3] c) Is the model adequate (good enough) in explaining or predicting delivery cost? Justify with appropriate measure by explaining exactly what it means. [3] d) Is the model significant at 5% level in explaining or predicting delivery cost for a consignment? Justify with appropriate measure from the outputs. [3] e) Is distance (X1) between the pick-up point and destination an individual significant predictor of delivery cost (Y) in the model? Justify with appropriate measure from the outputs. [3] f) Find out the missing values 'a' and 'b' given in the output of Table 2. [2]2. [Marks:10] Interval Estimation: A small scale restaurant owner wants to find an estimate of the average daily profit. For this, he randomly selected 25 days from the past year's entry log and collected the following observations: a. Sample mean of the daily profits for those 25 selected days = Rs. 33892 b. Sample standard deviation of the daily profits for those 25 selected days = Rs. 435 Assuming that daily profit values follow normal distribution, answer the following questions: a) What is the target population? [1] b) What is the population parameter that needs to be estimated? [1] c) Find a 95% confidence interval for the population mean (average daily profit). [4] d) How do you interpret this confidence interval obtained in 2.c)? [2] e) Find a 95% confidence interval for the population mean (average daily profit) if the sample size is 100 instead of 25. [2]