payton collected data to show the relationship between the number of hours he practices and the number of…

Answer:

-4.5

Explanation:

Step1: Recall slope formula

$m=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n}(x_i-\bar{x})^2}$ Let $x$ be the number of hours and $y$ be the number of errors. $\bar{x}=\frac{1 + 2+3+4+5+6+7+8}{8}=\frac{36}{8} = 4.5$ $\bar{y}=\frac{36+34+30+31+23+16+11+5}{8}=\frac{186}{8}=23.25$

Step2: Calculate numerator terms

For $(x_1,y_1)=(1,36)$: $(1 - 4.5)(36 - 23.25)=(-3.5)\times12.75=-44.625$ For $(x_2,y_2)=(2,34)$: $(2 - 4.5)(34 - 23.25)=(-2.5)\times10.75=-26.875$ For $(x_3,y_3)=(3,30)$: $(3 - 4.5)(30 - 23.25)=(-1.5)\times6.75=-10.125$ For $(x_4,y_4)=(4,31)$: $(4 - 4.5)(31 - 23.25)=(-0.5)\times7.75=-3.875$ For $(x_5,y_5)=(5,23)$: $(5 - 4.5)(23 - 23.25)=(0.5)\times(-0.25)=-0.125$ For $(x_6,y_6)=(6,16)$: $(6 - 4.5)(16 - 23.25)=(1.5)\times(-7.25)=-10.875$ For $(x_7,y_7)=(7,11)$: $(7 - 4.5)(11 - 23.25)=(2.5)\times(-12.25)=-30.625$ For $(x_8,y_8)=(8,5)$: $(8 - 4.5)(5 - 23.25)=(3.5)\times(-18.25)=-63.875$ Sum of these products $\sum_{i = 1}^{8}(x_i-\bar{x})(y_i - \bar{y})=-181$

Step3: Calculate denominator terms

$(1 - 4.5)^2=(-3.5)^2 = 12.25$ $(2 - 4.5)^2=(-2.5)^2 = 6.25$ $(3 - 4.5)^2=(-1.5)^2 = 2.25$ $(4 - 4.5)^2=(-0.5)^2 = 0.25$ $(5 - 4.5)^2=(0.5)^2 = 0.25$ $(6 - 4.5)^2=(1.5)^2 = 2.25$ $(7 - 4.5)^2=(2.5)^2 = 6.25$ $(8 - 4.5)^2=(3.5)^2 = 12.25$ Sum of these squares $\sum_{i=1}^{8}(x_i-\bar{x})^2 = 40.5$

Step4: Calculate slope

$m=\frac{-181}{40.5}\approx - 4.5$