Finding the best rule

Let's use the prediction rule where m = 1.0 and to estimate the weight for the player with height = 70 in.

So his predicted weight is

Y' = 1 x 70 + 102 = 172.

(Note from the table that his actual weight is 170. Our prediction rule is working rather well.)

The predicted weights for all 17 of the heights are given in the table below. Look at the graph and make sure that you find the corresponding values to what is here in the table.

**Table 2**
	Height,	Weight	Predicted
	X	Y	Weight, Y'
	61	140	163
	64	141	166
	64	144	166
	66	158	168
	67	156	169
	67	174	169
	68	160	170
	68	164	170
	68	170	170
	69	172	171
	70	170	172
	71	175	173
	72	170	174
	72	174	174
	73	176	175
	74	180	176
	75	192	177
Median:	68	170
Mean:			170.76

slope = 1 int = = 102 equation is Y'= 1.0 * X + 102

How do you think the fit of this line to the data looks? Look at the corresponding graph as well.

Let's see what the predicted weights are for another slope.

Let's use the prediction rule where m = 2.0 to estimate the weight for the player with height = 70 in.

So his predicted weight is

Y' = 2 x 70 + 34 = 174.

(Note from the table that his actual weight is 170.)

The predicted weights for all 17 of the heights are given in the table below. Look at the graph and make sure that you find the corresponding values to what is here in the table.

**Table 3**
	Height,	Weight	Predicted
	X	Y	Weight, Y'
	61	140	156
	64	141	162
	64	144	162
	66	158	166
	67	156	168
	67	174	168
	68	160	170
	68	164	170
	68	170	170
	69	172	172
	70	170	174
	71	175	176
	72	170	178
	72	174	178
	73	176	180
	74	180	182
	75	192	184
Median:	68	170
Mean:			171.53

slope = 2 int = = 34 equation is Y'= 2.0 * X + 34

How do you think the fit of this line with slope=2 to the data looks? Look at the corresponding graph as well.

Exercises:

For each slope given below, use the football player spreadsheet to find the corresponding predicted values for players' weights.

Use m = -1; m = 0; m = +1.0; m= +2.0; m= +3.0; m= +3.5; m=+4.0

For these slopes, which do you think give the best prediction rule ?

Crickets, anyone

Use the cricket spreadsheet you created in the previous section for the following.

Based on the slope you selected in the previous section, choose at least 5 more slopes and find the equation of each line for the slopes you chose. Also, find the corresponding values for the predicted temperatures based on these equations.

Which slope and equation do you think gives the best prediction rule?

Continue to the next section: Mean Prediction Error.