Use the equation of the least-squares line to make predictions.

A market researcher models the relationship between years since launch (x) and annual sales (y, in thousands of units) for a new product. Data from the first seven years gives the least-squares line equation y = 23.8 + 6.4x, with a coefficient of determination, R² = 0.88. (a) Use the equation of the least-squares line to predict the annual sales in year 10. (2 marks) (b) The product will be discontinued if annual sales fall below 50,000 units. Evaluate the reasonableness of continuing the product to year 10, based on your prediction in part (a) and the strength of the linear model. (2 marks)

A local cinema analysed the relationship between the number of cinema tickets sold per week and the average daily temperature during that week. The least-squares line equation for this data is $y = 8.2x + 156$, where $x$ is the average daily temperature in degrees Celsius and $y$ is the number of tickets sold per week. (a) Use the equation to predict the number of tickets sold in a week when the average daily temperature is $18°C$. (1 mark) (b) In another week, the average daily temperature is $24°C$. Use the equation to predict the number of tickets sold. (1 mark) (c) State one limitation of using this equation to make predictions. (1 mark)