Manufacturer Screen Size (inches) Price (S) Sharp 46 736.5 Samsung 52 1150 Samsung 46 895 Sony 40 625 Sharp Samsung Samsung Sharp 42 773.25 46 961.25 40 686 37 574.75 Sharp 46 1000 Sony 40 722.25 Sony 52 1307.5 Samsung 32 373.75 Sharp 37 657.25 Sharp 32 426.75 Sharp Samsung 52 1389 40 874.75 Sharp Samsung 32 517.5 52 1475 Sony 40 954.25 Sony 52 1551.5 Sony 46 1303 Sony 46 1430.5 Sony 52 1717
Does there appear to be a positive or negative relationship between price and screen size? Use a
Question 1: Determine and interpret the
- Value of correlation coefficient:
- Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
Question 2: Estimate the relationship between screen size and price using a simple linear regression model and interpret the estimated coefficients. In your interpretation, tell the dollar amount by which price will change for each unit of increase in screen size. (The answer for the second part of this question will come from coefficients of screen size)
Adjusted R squared value:
Interpretation of coefficient: With every unit increase in screen size, the price will increase by __________? The interpretation value will come from the 2nd column of your results.
Question 3:
Multiple linear regression: Include the manufacturer dummy variable (Samsung=1, 0 otherwise) and estimate the relationship between screen size, price and manufacturer dummy as a multiple linear regression model. Regression equation:
Price = Intercept + Screen Size x Slope Coefficient of Screen size + Manufacturer brand x Slope Coefficient of Manufacturer Brand, Provide your answer in the form of above regression equation. But replace the underlined parts with numerical values from your
Question 4: Interpret the slope coefficients and their significance (p-value) from your output in the above answer. Include the following in your interpretation: Is the relationship between screen size and price positive, negative, or zero? Is the relationship between screen size and price statistically significant? Is the relationship between brand and price (Samsung or not Samsung) statistically significant? Slope coefficients (these values come from 2nd column of the results at the bottom).
Interpretation of slope coefficients: With every unit increase in screen size, the price will (choose one: increase / decrease by) _____ and when brand is Samsung, price will be (choose one: higher / lower by) ________?*
Significance (p-value): significant is less than 5%
* When the coefficient values are positive, the value of the dependent variable will increase by the corresponding coefficient value. Conversely, when the coefficient values are negative, the value of the dependent variable will decrease by the same amount. For example, if the coefficient is +40, it indicates that the price will increase by $40. However, if the coefficient is -40, it indicates that the price will decrease by $40.
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