Question

In: Statistics and Probability

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

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

  1. 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

  1. 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

  1. 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

Solutions

Expert Solution

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.


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