Least Squares

Plug In One x

The fitted line is a rule that can be evaluated at a displayed x value. This lesson substitutes one exact x and reads the exact fitted line value.

highlighted = computed this step

Start with the fitted rule

The fitted line from the shown data is y-hat=11/10 plus 11/10x.

y^=11/10+11/10x\hat y=11/10+{}11/10x
Plug one x into the fitted lineA single displayed x value is substituted into the exact fitted line.Plug one x into the fitted linex=4exact substitutionfity=11/10+11/10xx4sub11/10+11/10*4yhat11/2line value from fitted ruleshown-data arithmetic only

Plug in one x

Use the displayed x=4. Substitution gives 11/10 plus 11/10 times 4.

y^=11/10+11/10⋅4\hat y=11/10+{}11/10\cdot4
Plug one x into the fitted lineA single displayed x value is substituted into the exact fitted line.Plug one x into the fitted linex=4exact substitutionfity=11/10+11/10xx4sub11/10+11/10*4yhat11/2line value from fitted ruleshown-data arithmetic only

Read the exact line value

The exact line value is y-hat=11/2. This is a value from the fitted rule for one displayed x, not proof about future rows.

y^=11/2\hat y=11/2
Plug one x into the fitted lineA single displayed x value is substituted into the exact fitted line.Plug one x into the fitted linex=4exact substitutionfity=11/10+11/10xx4sub11/10+11/10*4yhat11/2line value from fitted ruleshown-data arithmetic only