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Q49.
Expert-verifiedThe table shows the number of sales made at an outerwear store during a sale. Write an equation of the regression line. Then estimate the daily sales on day 10 of the sale
Days Since Sale Began | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Daily Sales ($\$$) | 15 | 21 | 32 | 30 | 40 | 38 | 51 |
The required equation of the regression line is: $\mathit{y}\mathbf{=}\mathbf{5}\mathbf{.36}\mathit{x}\mathbf{+}\mathbf{11}$. The daily sales on day 10 of the sale is $\$$65.
Let
$X$-axis = days since sale begin.
$Y$-axis = daily sales ($\$$).
Using the regression calculator to find the equation of the regression line:
Days since sale began ($x$) | Daily Sales ($y$) |
1 | 15 |
2 | 21 |
3 | 32 |
4 | 30 |
5 | 40 |
6 | 38 |
7 | 51 |
$\begin{array}{l}\text{Sum of}X=28\\ \text{Sum of}Y=227\\ \text{Mean}X=4\\ \text{Mean}Y=32.4286\\ \text{Sum of squares}\left(S{S}_{X}\right)=28\\ \text{Sum of products}\left(SP\right)=150\end{array}$
Regression Equation: $\u0177=bX+a$
role="math" localid="1647412399173" $\begin{array}{l}b=SP/S{S}_{X}=150/28=5.35714\\ a={M}_{Y}-b{M}_{X}=32.43-(5.36\times 4)=11\\ y=5.35714X+11\end{array}$
Graph the line $\widehat{y}=5.35714X+11$ with slope $a$ and intercept $b$.
Thus, the regression equation is $\widehat{y}=5.36X+11$.
Substituting the value of $x=10$ in regression equation to find the daily sales on day 10 of the sale :
$\begin{array}{c}\widehat{y}=5.36X+11\\ \widehat{y}=5.36\left(10\right)+11\\ \widehat{y}=53.6+11\\ \widehat{y}=64.6\approx 65\end{array}$
So, the daily sales on day 10 of the sale = $\$$65.
The table below shows the relationship between certain temperatures in degrees Fahrenheit and degrees Celsius. Which of the following linear equations correctly models the relationship?
Celsius (C) | Fahrenheit (F) |
$10\xb0$ | $50\xb0$ |
$15\xb0$ | $59\xb0$ |
$20\xb0$ | $68\xb0$ |
$25\xb0$ | $77\xb0$ |
$30\xb0$ | $86\xb0$ |
F $F=\frac{8}{5}C+35$
G $F=\frac{4}{5}C+42$
H $F=\frac{9}{5}C+32$
J $F=\frac{12}{5}C+26$
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