Question

2. An accountant for a small manufacturing plan t collected the following random sample to study the the selling price. Round all your relationship between x answers to one decimal place. cular item and y the cost to make a part 47 23 52 71 78 128 70 152 198 a. [4 pts] Create a scatter diagram. (2 pts] Using only the scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Explain your answer 4pts] Find the equation of the least squares line if the line crosses the y-axis at $7.7 and the ean point of this data set is (t,y) (44.8, 126.3). The standard deviations of x and y are $17.9 d $47.6, respectively.

Answer 1

2(a)

2(b)

It is seen that as x($) increases, y($) also increases. Thus it can be said that there is a positive correlation.

2(c)

The least square line is represented as

y = a + bx

where a=intercept on y-axis, b=slope

From the normal equations it is obtained that a = - b => b = (-a)/

From the problem it is given that a=7.7, =44.8,  =126.3 => b = (126.3 - 7.7)/44.8 = 2.65

Therefore we get the least square line as

y = 7.7 + 2.65 x

2(d)

We get the least square line as y = 7.7 + 2.65 x

Now x = $35

Therefore y = $(7.7 + 2.65*35) = $100.45 $100.40

The least square line predicts the selling price of a particular item to be $100.40 when to cost to make it is $35.