elijah is saving up for a new pair of sneakers. he tracks how much money he has in his savings account at the end of each week and plots the data on a scatterplot to see how his savings are growing over time.

question 4

based on your line, how much do you predict elijah will have at the end of week 12?

enter your response here

Question

elijah is saving up for a new pair of sneakers. he tracks how much money he has in his savings account at the end of each week and plots the data on a scatterplot to see how his savings are growing over time.

question 4

based on your line, how much do you predict elijah will have at the end of week 12?

enter your response here

question 4

based on your line, how much do you predict elijah will have at the end of week 12?

enter your response here

Accepted Answer

# Explanation:
## Step1: Calculate the mean of Week ($x$) and Amount Saved ($y$)
Let $x$ be the week number and $y$ be the amount saved.
$\bar{x}=\frac{1 + 2+3+4+5+6+7+8+9+10}{10}=\frac{55}{10} = 5.5$
$\bar{y}=\frac{10 + 18+26+29+40+47+51+56+75+63}{10}=\frac{415}{10}=41.5$

## Step2: Calculate the slope ($b$)
$$
\begin{align*}
b&=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}\
\sum_{i = 1}^{10}(x_{i}-\bar{x})(y_{i}-\bar{y})&=(1 - 5.5)(10 - 41.5)+(2 - 5.5)(18 - 41.5)+(3 - 5.5)(26 - 41.5)+(4 - 5.5)(29 - 41.5)+(5 - 5.5)(40 - 41.5)+(6 - 5.5)(47 - 41.5)+(7 - 5.5)(51 - 41.5)+(8 - 5.5)(56 - 41.5)+(9 - 5.5)(75 - 41.5)+(10 - 5.5)(63 - 41.5)\
&=(- 4.5)(-31.5)+(-3.5)(-23.5)+(-2.5)(-15.5)+(-1.5)(-12.5)+(-0.5)(-1.5)+(0.5)(5.5)+(1.5)(9.5)+(2.5)(14.5)+(3.5)(33.5)+(4.5)(21.5)\
&=141.75 + 82.25+38.75 + 18.75+0.75+2.75+14.25+36.25+117.25+96.75\
&=550\
\sum_{i = 1}^{10}(x_{i}-\bar{x})^{2}&=(1 - 5.5)^{2}+(2 - 5.5)^{2}+(3 - 5.5)^{2}+(4 - 5.5)^{2}+(5 - 5.5)^{2}+(6 - 5.5)^{2}+(7 - 5.5)^{2}+(8 - 5.5)^{2}+(9 - 5.5)^{2}+(10 - 5.5)^{2}\
&=(-4.5)^{2}+(-3.5)^{2}+(-2.5)^{2}+(-1.5)^{2}+(-0.5)^{2}+(0.5)^{2}+(1.5)^{2}+(2.5)^{2}+(3.5)^{2}+(4.5)^{2}\
&=20.25+12.25 + 6.25+2.25+0.25+0.25+2.25+6.25+12.25+20.25\
&=82.5\
b&=\frac{550}{82.5}\approx6.67
\end{align*}
$$

## Step3: Calculate the intercept ($a$)
$a=\bar{y}-b\bar{x}=41.5-6.67\times5.5 = 41.5 - 36.685=4.815$

## Step4: Form the regression equation
The regression equation is $y = 4.815+6.67x$

## Step5: Predict for $x = 12$
When $x = 12$, $y=4.815+6.67\times12=4.815 + 80.04=84.855\approx85$

# Answer:
$85$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the mean of Week ($x$) and Amount Saved ($y$)

Step2: Calculate the slope ($b$)

Step3: Calculate the intercept ($a$)

Step4: Form the regression equation

Step5: Predict for \(x = 12\)

Answer: