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A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year $ per capita 2 32.21 3 37.81 4 43.32 6. 49.62 34.09 44.67 51.88 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 32.21 34.09 37.81 43.32 44.67 34.09 44.67 37.81 49.62 51.88 43.32 49.62 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a 4.6884 b0.9650 If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.) $ (41.36 ]× per capita (c) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) r(0.9615 0.9245 Test p>0 at the 1% level of significance. (Use 2 decimal places.) t7.00 critical t|5.60

A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year $ per capita 2 32.21 3 37.81 4 43.32 6. 49.62 34.09 44.67 51.88 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 32.21 34.09 37.81 43.32 44.67 34.09 44.67 37.81 49.62 51.88 43.32 49.62 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a 4.6884 b0.9650 If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.) $ (41.36 ]× per capita (c) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) r(0.9615 0.9245 Test p>0 at the 1% level of significance. (Use 2 decimal places.) t7.00 critical t|5.60

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2CYU
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A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year $ per capita 1 2 3 4 6. 7 32.21 34.09 37.81 43.32 44.67 49.62 51.88 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 44,67 43.32 44.67 32.21 34.09 37.81 49.62 y34.09 37.81 43.32 49.62 51.88 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a 4.6884 b0.9650 If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.) $ 41.36 ]× per capita (c) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) r0.9615 0.9245 Test p>0 at the 1% level of significance. (Use 2 decimal places.) t7.00 critical t 5.60
Transcribed Image Text:A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year $ per capita 1 2 3 4 6. 7 32.21 34.09 37.81 43.32 44.67 49.62 51.88 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. 44,67 43.32 44.67 32.21 34.09 37.81 49.62 y34.09 37.81 43.32 49.62 51.88 (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ý = a + bx. (Use 4 decimal places.) a 4.6884 b0.9650 If the per capita spending was x = $38 one year, what do you predict for the spending the next year? (Use 2 decimal places.) $ 41.36 ]× per capita (c) Compute the sample correlation coefficient r and the coefficient of determination 2. (Use 4 decimal places.) r0.9615 0.9245 Test p>0 at the 1% level of significance. (Use 2 decimal places.) t7.00 critical t 5.60
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