Question

An automobile company is running a new television commercial in five cities with approximately the same population. the following table shows the number of times
the commercial is run on tv in each city and the number of car sales in hundreds). find the linear regression line for the data given in the table. round any intermediate
calculations to no less than six decimal places, and round the coefficients to two decimal places.
number of tv commercials, x
car sales, y (in hundreds)
13 6 12 14 17
3 28 97

Answer 1

The linear regression equation is y = 0.50x - 0.36

How to determine the linear regression equation?

The proper format of the table of values is:

Number of tv commercials, x: 13 6 12 14 17

Car sales, y (in hundreds):        3  2 8   9  7

Next, we determine the linear regression equation using a graphing calculator.

From the graphing calculator, we have the following summary:

• Sum of X = 62
• Sum of Y = 29
• Mean X = 12.4
• Mean Y = 5.8
• Sum of squares (SSX) = 65.2
• Sum of products (SP) = 32.4

The regression equation is the calculated as:

y = bx + a

Where

b = SP/SSX = 32.4/65.2 = 0.49693

a = MY - bMX = 5.8 - (0.5*12.4) = -0.36196

Substitute these values in y = bx + a

y = 0.49693x - 0.36196

Approximate

y = 0.50x - 0.36

Hence, the linear regression equation is y = 0.50x - 0.36

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