Question

Answer the questions based on the results of the t-shirt sales analysis shown by the regression calculator. if the t-shirts are priced at $13 each, what is a reasonable prediction for the number sold? 10 t-shirts 15 t-shirts 18 t-shirts 20 t-shirts

Answer 1

The Linear Regression Equation has the form Y= a + bX. The reasonable prediction for the number of t-shirts sold is 18.

What is the Linear Regression Equation?

The Linear Regression Equation has the form Y= a + bX, where Y is the dependent variable (that's the variable that goes on the Y-axis), X is the independent variable (i.e. it is plotted on the X-axis), b is the slope of the line and a is the y-intercept.

In order to calculate the reasonable prediction for the number of t-shirts sold, we need to find the function of the given graph below.

As we can see that the function of the graph is linear(line), therefore, we take two points, to find the value of the slope and the value of the constant.

$(x_1,y_1)=(10,25)\\(x_2,y_2)=(15,12)$

The value of the slope can be written as,

$m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{12-25}{15-10}=\dfrac{-13}{5}$

Now, substitute the value of any one point in the equation of the line,

$y=mx+c\\\\y_1=\dfrac{-13}{5}x_1+c\\\\25=(\dfrac{-13}{5}\times 10)+c\\\\25=-26+c\\\\51=c$

As the price of the t-shirt is $13, therefore, the value of y(or the reasonable prediction for the number of t-shirts sold) can be found,

$y=\dfrac{-13}{5}x+51\\\\y =(-2.6 \times 13)+51\\\\y = 17.2$

The value of the reasonable prediction for the number of t-shirts sold is 17.2 which is close to 18.

Hence, the reasonable prediction for the number of t-shirts sold is 18.

Learn more about Linear Regression Equation:

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