2.3-2.4 solutions

# Slope 04975 y intercept line is change for year 082

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Slope = = 0.4975 Y intercept = Line is: Change for year = .082 + .4975 times change in Jan. *18. Give 2 statistical reasons why you know this relationship is positive. The correlation and the slope are both positive. 3

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19. Explain why you think the relationship between X and Y is so strong in this problem (in other words why is the correlation so high?) January must set the tone for the year in terms of stock market index changes. Here are data for calories and salt content (milligrams of sodium) in 17 brands of meat hot dogs: Sodium (mg) Calories 600 500 400 300 200 100 200 180 160 140 120 100 Scatterplot of Calories vs Sodium (mg) 20. A computer found the regression equation for the above problem is Calories = 61.6 + 0.232 Sodium (mg). How do we interpret the slope of this line? a. As the amount of sodium increases by 1 milligram, the calories increase by 0.232 b. As the amount of sodium increases by 1 milligram, the calories increase by 61.6 c. As the amount of calories increases by 1, the sodium increases by 0.232 milligrams d. As the amount of calories increases by 1, the sodium increases by 61.6 milligrams. 21. Interpret the Y-intercept. Does it make sense here? Y intercept = 61.6, which for a hot dog with 0 mg of sodium the calories are predicted to be 61.6. This prediction is not going to be an appropriate prediction to make though because the data collected starts at just over 100mg for the values of X (sodium) and 0 is no where near this value. 22. For what range of sodium can you make a good prediction about calories? looking at the X values on the scatterplot, making calorie predictions for hot dogs with between 150 to 550 mg of sodium would be appropriate. Suppose the age of a woman is strongly correlated with the age of her husband when both are marrying for the 2nd time. Variable N Mean StDev Min Max Woman’s Age 28 31.24 9.49 17.06 58.97 Husband’s Age 28 35.79 8.86 14.00 51.00 Pearson’s Correlation: 0.9586 4
23. There is a positive linear relationship between these two variables. Explain why this makes sense in the context of this problem. Older women tend to marry older men and younger women tend to marry younger men. *24 . Suppose you want to use the woman’s age to predict her husband’ age. Find the slope of the regression line. X=wife’s age and Y=husband’s age (this is important!) Slope = .895 (as the wife’s age increases by 1 year, the husband’s age increases by .895 years) *25. Suppose you want to use the husband’s age to predict the woman’s age. Find the slope of the regression line. --X = husband, Y = wife (this is important!) Slope = = 1.027. As the husband’s age increases by 1 year, the wife’s age increases by 1.027 years, on average. Suppose a manufacturer has recorded its cost of electricity (in dollars) and the total number of hours of machine time for their factory during a certain number of weeks. They want to use the data to estimate electric bills based on machine time. Their new statistician analyzed the data. The results are shown below. Descriptive Statistics: Time, Cost Variable N Mean SE Mean StDev Variance Minimum Q1 Median Time 52 10.865 0.369 2.664 7.099 6.000 8.000 11.000 Cost 52 1041.9 35.9 258.9 67043.1 464.3 879.2 1018.8 Variable Q3 Maximum Time 13.000 15.000 Cost 1243.2 1598.1 Pearson’s Correlation: 0.7375 26. Based on the above output, a scatterplot of this data set that will be used for prediction purposes would have which variable on which axis?

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