Question

Se the following information for problems 26 through 29. R&D engineers for a car manufacturer wanted to test the gas mileage y (mpg) using reg conditions and the following gas mileage was observed. relationship between a cars speed x (mph) and its ular unleaded gas. The car was driven at different speeds in controlled Speed, x 30 40 50 60 70 27 90 22 80 39 383632 24 26) What kind of relationship is suggested by a scatter plot for the data above? a. Non-linear b. Parabolic c. Normal d. Linear 27) What is the correlation coefficient indicated by the relationship? a. t0.75449 b. 0.985349 c. -0.985349 d. -0.3142857 28) What kind of mpg should you expect if they drove at 66 mph? a. 29 b. 31 c. 27 d. 30 29) For every 1 mph increase in speed, what effect would you see in mpg? a. gas mileage should improve slightly, about 1/3 mpg. b. gas mileage should be reduced slightly, about 1/3 mpg. c. gas mileage should remain about the same. d. gas mileage is not dependent on speed driven

Answer 1

Q 26) Use MINITAB to get the scatter plot of the given data is given below:

Scatterplot of mpg y vs Speed x Scatterplot of mpg y vs Speedx 40 35 e 30 25 20-L 70 80 90 60 Speed x 30 40 50

Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. However, they have a very specific purpose. Scatter plots show how much one variable is affected by another.
The relationship between two variables is called their correlation .
Scatter plots usually consist of a large body of data. The closer the data points come when plotted to making a straight line, the higher the correlation between the two variables, or the stronger the relationship.
If the data points make a straight line going from the origin out to high x- and y-values, then the variables are said to have a positive correlation . If the line goes from a high-value on the y-axis down to a high-value on the x-axis, the variables have a negative correlation .

The above scatter plot shows an negative linear relationship between speed and mpg.
OPTION D.

Q 27) Use MINITAB to get the value of the correlation the output is:

Correlations: Speed x, mpg y Pearson correlation of Speed x and mpg y - -0.985 P-Value 0.000

If the line goes from a high-value on the y-axis down to a high-value on the x-axis, the variables have a negative correlation
OPTION C

Q 28) The regression line is given by:

. Regression equation: У-bo + bix, where S. and rx

Use MINITAB to get the following output is:

Regression Analysis: mpg y versus Speed x The regression equation is mpg y-50.0-0.314 Speed x Predictor Constant 50.000 1.539 32.50 0.000 Speed x 0.31429 0.02433 -12.92 0.000 Coef SE Coef S-1.28730 R-Sq 97.1% R-Sq (adj ) -96.5% - Analysis of Variance Source DF MS Regression 1 276.57 276.57 166.90 0.000 Residual Error 5 8.291.66 Total 6 284.86

calculate the mpg when thee speed 66mph to get teh following:

$mpg y = 50.0 - 0.314 Speed x= 50.0 - (0.314 *66)=29.276\sim 29$
OPTION A

Q 29) The above regresssion line shows when the slope of the regression that is speed is increase 1 mph then mpg will decrease slightly about 1/3 mpg.since slope is negative.
OPTION B