Consider the following time series. t 1 2 3 4 5 6 7 121 111 105 99 95 93 89 (a) Construct a time series plot. What type of pattern exists in the data? O The time series plot shows a linear trend. O The time series plot shows a seasonal pattern. O The time series plot shows a nonlinear trend. O The time series plot shows a horizontal pattern. (b) Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. (Round your answers to two decimal places.) bo = b, = -5.07 (c) What is the forecast for t = 8? (Round your answer to one decimal place.)
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- 1. Consider the following time series: a. Construct a time series plot. What type of pattern exists in the data? b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.The below time series gives the indices of Industrial Production in U.S for 10 consecutive years. Year IP 1 79.62 2 86.54 3 88.14 4 89.23 5 93.45 6 97.4 7 99.34 8 96.98 9 100.22 10 103.56 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. c. What is the forecast for t = 11?The president of small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm’s leading product over the past eight years. Year Cost/Unit ($) Year Cost/Unit ($) 1 20.00 5 26.60 2 24.50 6 30.00 3 28.20 7 31.00 4 27.50 8 36.00 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. What is the average cost increase that the firm has been realizing per year? Compute an estimate of the cost/unit for next year.
- Consider the following time series: a. Construct a time series plot. What type of pattern exists in the data?b. Use simple linear regression analysis to find the parameters for the line that minimizesMSE for this time series.c. What is the forecast for t 5 6?The below time series gives the indices of Industrial Production in U.S for 10 consecutive years. Year IP 1 79.62 2 86.54 3 88.14 4 89.23 5 93.45 6 97.4 7 99.34 8 96.98 9 100.22 10 103.56 Construct a time series plot. What type of pattern exists in the data? Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. What is the forecast for t = 11?A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…
- Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 2 3 6 3 3 5 6 4 5 7 8 Choose the correct time series plot. (i) (ii) (iii) (iv) - Plot (iii) What type of pattern exists in the data?- Horizontal Pattern with Seasonality Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)Value = fill in the blank 3 + fill in the blank 4 Qtr1 + fill in the blank 5 Qtr2 + fill in the blank 6 Qtr3 + fill in the blank 7 t Compute the quarterly forecasts for next year. If…Consider the following time series data. Quarter Year 1 Year 2 Year 3 1 4 6 7 2 0 1 4 3 3 5 6 4 5 7 8 (a) Choose the correct time series plot. (i) (ii) (iii) (iv) What type of pattern exists in the data? (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). If the constant is "1" it must be entered in the box. Do not round intermediate calculation. ŷ = + Qtr1 + Qtr2 + Qtr3 (c) Compute the quarterly forecasts for next year based on the model you developed in part (b). If required, round your answers to three decimal places. Do not round…The table shows a part of an output of a linear regression model predicting the average fare on different flight routes. Data Table Regression Table Coefficient Constant 95.80976147 COUPON −9.61654124 DISTANCE 0.080733811 PAX −0.000167343 What is the difference in prediction of the following two routes? Route A that is 3,000 miles, with COUPON=1.5 and PAX=6,000 Route B that is 3,000 miles, with COUPON=1.2 and PAX=6,000.
- Consider a simple linear regression model Y=α+βX+ε. We have collected 15 samples, from which we calculated the summary statistics ∑xi=66, ∑x2i=6568, ∑yi=459, ∑y2i=27933, ∑xiyi=11311. Suppose one of the data is supposed to be (x1=10, y1=30), but is incorrectly recorded as (x1=7, y1=34). All other observations are correctly recorded. What is the OLS estimators αˆ= ? and βˆ= ? based on the correct data.Consider the following time series. t 1 2 3 4 5 6 7 Tt 120 110 100 96 94 92 88 Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300)y-intercept, b0= Slope, b1 = MSE = What is the forecast for t= 8? If required, round your answer to three decimal places.method that uses a weighted average of past values for arriving at smoothed time series values is known as ______. a. decomposition b. regression analysis c. exponential smoothing d. deseasonalization