Predicting tropical storms William Gray heads the Tropical Meteorology Project at Colorado State

University. His forecasts before each year’s hurricane $2008$season attract lots of attention. Here are data on the number of named Atlantic tropical storms predicted by Dr. Gray and the actual number of storms for the years $1984$ to 2008:

Analyze these data. How accurate are Dr. Gray’s forecasts? How many tropical storms would you expect in a year when his preseason forecast calls for $16$ storms? What is the effect of the disastrous $2005$ season on your answers? Follow the four-step process.

Linear regression is commonly used for predictive analysis and modeling.

To begin, plot the forecast (X) as an explanatory variable and the actual number of storms as the response variable in a scatterplot. Fit a least-squares line to the data if the graph has a linear form. Then plot the residuals. The residuals$r^2$ and s indicate how well the line fits the data and the magnitude of our prediction mistakes. A scatterplot of the data is shown in the diagram below. The scatterplot reveals a positive relationship. In other words, if there are more forecasts, there are more actual storms. The entire pattern is relatively linear ($r=0.5478$ according to a calculator). On the scatterplot in the $Y-$direction, there is one outlier.

Using the MINITAB, the regression equation is shown below

The least-square equation is $y=1.69+0.915X$

Using the MINITAB, the residual plot is shown below:

The slope indicates that the actual forecast increased by $0.915$ for each additional forecast. The $Y-$intercept is the value of $Y$ when $X=0$; for example, if the forecast is $O$, the actual storm number will be 1. The residual plot was used. The scatter points around the "residual = $0$" line are rather "random," with one extremely large positive residual (point for the year $2005$). On the forecast scale, the majority of the prediction mistakes (residuals) are 10 points or less. The standard error of the residuals was calculated to be $s=3.9983$ This is around the amount of an average regression line prediction error. Since $=0.3001$, the least-squares model has accounted for $30.01$ percent of the variation in the actual number of storms.

Use the equation

Actual storm $=1.69+0.915$(forecast)

To estimate the number of storms that will occur based on the prediction. However, our projections may not be particularly accurate. It's risky to make predictions with this model. If Dr. Gray's preseason prediction is correct, then

Actual storm

Consider the below figure:

The outcome of eliminating the $2005$season from the correlation and regression line is seen in the graph above. One extra regression line is added to the graph once the $2005$season has ended. Removing this point has no influence on the regression line, as can be shown.

Therefore, DR.G’s forecasts are not very accurate. There are $16$tropical storms. The effect disastrous has a little effect.