Final answer:
To forecast data with a linear trend, linear regression is used to fit a line of best fit by plotting the data on a time series graph, calculating the line's slope and y-intercept, and using this to predict future data points, while considering outliers and the strength of the linear relationship with correlation.
Step-by-step explanation:
When forecasting data with a linear trend, the moving average method may not be appropriate because it is better-suited for stationary data without trends or seasonality. Instead, a method that takes into account the trend component should be used. One such method is linear regression, which involves fitting a line to the data points. This line, known as the line of best fit, minimizes the sum of the squared differences between the observed values and the values predicted by the line.
The first step is to plot the data on a time series graph, where the x-axis represents time, and the y-axis represents the variable of interest. Observe the plotted points to determine if they suggest a linear relationship. If the trend appears to be linear, you would proceed by calculating the slope and y-intercept of the least-squares line. The slope describes the rate of change over time, while the y-intercept is the value when time equals zero.
After computing these parameters, you can use the equation of the line (y = mx + b) to make future forecasts. It's essential to consider whether there are outliers that could affect the slope and intercept, making the predictions less reliable. In addition, the validity of a linear regression model for forecasting should be considered before applying it to data points well outside of the range of observed values. Using correlation, one can assess the strength of the relationship between the time and the variable of interest.