Question

1. Listed below are sizes (in thousands of square feet) and revenue (in millions of dollars) from casinos in Atlantic City.

SIZE (x) 180 227 140 144 161 147 141

REVENUE (y) 150 157 140 127 123 106 101

a) SKETCH THE SCATTERPLOT

b) DOES IT APPEAR TO BE POSITIVE OR NEGATIVE?

c) DOES IT APPEAR TO BE WEAK, MODERATE, OR STRONG ?

d) FIND THE LINEAR CORRELATION COEFFICIENT r

e) FIND r2 AND INTERPRET

f) FIND THE LINEAR REGRESSION AND GRAPH IT WITH THE DATA IN PART “a”

g) INTERPRET THE SLOPE OF THE REGEESSION LINE IN CONTEXT OF THE PROBLEM

h) USE THE LINEAR REGRESSION TO PREDICT THE REVENUE OF A 200,000 SQUARE FEET CASINO.

i) SHOULD YOU USE THE PREDICTION FOUND IN PART h, OR SHOULD YOU USE THE AVERAGE y? EXPLAIN

j) CALCULATE THE RESIDUAL OF A 147,000 SQUARE FEET CASINO.

k) SKETCH THE RESIDUAL PLOT

Answer 1

Let's use excel:

Step 1) First enter the given dataset in excel columns

step 2) Select both the column and then click on Insert >>>Scatter >>>First image

Then we get the following output:

b) From this output the we can say that there is positive correlation between X and Y.

c) From the scatterplot there is moderate correlation between x and y.

d) The linear correlation coefficient (r) is obtained by using "=CORREL(range of x, range of y)" this excel command.

and then enter

So, we get r = 0.727

e) coefficient of determination = r2 = 0.5285

About 52.85% variation in y is explain by the independent variable (x ).

f) Right click on any point on the scatter plot and choose "Add Trendline".