Tshirt Sales Prediction E40284

1. **State the problem:** We want to use the linear regression function $$y = 57.14x + 28.57$$ to predict the number of T-shirts sold in the years 2012, 2014, 2016, 2018, and 2020. 2. **Identify variables:** - $x$ is the number of years since 2010. - $y$ is the predicted number of T-shirts sold. 3. **Calculate $x$ for each year:** - For 2012: $x = 2012 - 2010 = 2$ - For 2014: $x = 2014 - 2010 = 4$ - For 2016: $x = 2016 - 2010 = 6$ - For 2018: $x = 2018 - 2010 = 8$ - For 2020: $x = 2020 - 2010 = 10$ 4. **Use the regression function to predict $y$:** - For 2012: $$y = 57.14(2) + 28.57 = 114.28 + 28.57 = 142.85$$ - For 2014: $$y = 57.14(4) + 28.57 = 228.56 + 28.57 = 257.13$$ - For 2016: $$y = 57.14(6) + 28.57 = 342.84 + 28.57 = 371.41$$ - For 2018: $$y = 57.14(8) + 28.57 = 457.12 + 28.57 = 485.69$$ - For 2020: $$y = 57.14(10) + 28.57 = 571.4 + 28.57 = 599.97$$ 5. **Compare predictions to actual data:** - Actual sales for 2012: 175 T-shirts; predicted: 142.85 (slightly low but reasonable) - Actual sales for 2014: 250 T-shirts; predicted: 257.13 (very close) - Actual sales for 2016: 375 T-shirts; predicted: 371.41 (very close) - Actual sales for 2018: no actual data given, prediction: 485.69 - Actual sales for 2020: no actual data given, prediction: 599.97 6. **Conclusion:** The linear regression function provides reasonable predictions for the years with actual data and can be used to estimate sales for future years like 2018 and 2020. **Final answers:** - 2012 prediction: approximately 143 T-shirts - 2014 prediction: approximately 257 T-shirts - 2016 prediction: approximately 371 T-shirts - 2018 prediction: approximately 486 T-shirts - 2020 prediction: approximately 600 T-shirts