Question

Use the data given below to answer the following question(s). The following table exhibits the age of second-hand furniture and the corresponding prices. Use the table to answer the following question(s). (Hint: Use scatter diagram and XLMiner where necessary.) Number of Years Values 2 1856 14 348 7 1020 5 1530 10 349 8 780 9 653 3 1830 10 750 6 1300 Q1. What is the relationship between the age of the furniture and their values? _ _________________ Q2. What is the regression equation that correctly expresses the relationship between the two variables? __ __________________ Q3. What is the expected value for a 8-year-old piece of furniture? __ __________________ Q4. What is the value for R2? ___

Answer 1

1. Let us make a scatter plot

Here we see that there is decreasing trend, which means for every increase in x there is corresponding decrease in y.

Hence there is negative correlation between x and y

Further we see that points lie nearby which means if line drawn mostly all will lie on the line, hence there is strong negative correlation between x and y

2.

Sum of X = 74
Sum of Y = 10416
Mean X = 7.4
Mean Y = 1041.6
Sum of squares (SS_X) = 116.4
Sum of products (SP) = -17307.4

Regression Equation = ŷ = bX + a

b = SP/SS_X = -17307.4/116.4 = -148.689

a = M_Y - bM_X = 1041.6 - (-148.69*7.4) = 2141.899

ŷ = -148.689X + 2141.899

3. For value for x=8, ŷ = (-148.689*8) + 2141.899=952.387

4. First we will find r

X Values
∑ = 74
Mean = 7.4
∑(X - M_x)² = SS_x = 116.4

Y Values
∑ = 10416
Mean = 1041.6
∑(Y - M_y)² = SS_y = 2855844.4

X and Y Combined
N = 10
∑(X - M_x)(Y - M_y) = -17307.4

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -17307.4 / √((116.4)(2855844.4)) = -0.949

So r^2=0.901

Hence 90.1% percentage of variation in y is explained by x