Question

A video media consultant collected the following data on popular LCD televisions sold through on-line retailers.

Manufacturer	Screen (in inches)	Price ($)
Sharp	34	459.50
Samsung	52	1,703.25
Samsung	36	733.00
Sony	36	729.75
Sharp	44	1,304.50
Samsung	36	700.00
Samsung	31	409.75
Sharp	35	639.75
Sharp	36	573.25
Sony	43	990.00
Sony	43	863.25
Samsung	40	814.00
Sharp	33	434.50
Sharp	31	455.00
Sharp	44	1,377.00
Samsung	46	1,298.25
Sharp	52	1,493.00
Samsung	50	1,698.50
Sony	33	487.25
Sony	38	691.25
Sony	33	489.00
Sony	41	863.25
Sony	51	1,477.00

  Click here for the Excel Data File

1. Does there appear to be a linear relationship between the screen size and the price? (Round your answer to 2 decimal places.)

_____ the correlation of screen and price is

2. Which variable is the "dependent" variable?

• Screen size

• Price

1. c-1. Use statistical software to determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Price=______+ screen size

1. c-2. Interpret the value of the slope in the regression equation. (Round your answer to 3 decimal places.)

For each __________ of one inch in screen size, the price increases

4. Include the manufacturer in a multiple linear regression analysis using a "dummy" variable. Does it appear that some manufacturers can command a premium price? Hint: You will need to use a set of indicator variables. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Price=________ + ___________ Screen+______________  Sony + __________ Sharp

5. Test each of the individual coefficients to see if they are significant. (Negative amounts should be indicated by a minus sign. Round your t-statistic to 2 decimal places and p-value to 4 decimal places.

Term T-value P-value

Constant

Screen

Sony

Sharp

Answer 1

We input this data set in MS Excel to answer the questions that follow.
(a) Correlation between screen and price = 0.97 (using the CORREL function).
(b) Price is the dependent variable.
(c-1) Price = 26.022 + 0.015 screen size (using the "Regression" option under Data > Data Analysis).
(c-2) For each increase of one inch in screen size, the price increases by $0.015.
(d) We now create the dummy variables for Sony and Sharp and carry out the regression analysis again (using the "Regression" option under Data > Data Analysis).
Price = 25.021 + 0.016 Screen + 1.755 Sony + 0.343 Sharp.
(e) The table is given below.

Term	T-value	P-value
Constant	21.91	0.0000
Screen	17.70	0.0000
Sony	1.91	0.0718
Sharp	0.37	0.7123

The screenshot of the output and the data set is given below.