Question

1. run a scatter plot for each of the two independent variables (IVs). The IVs are Temperature and Humidity. The dependent variable (DV) is “fuel economy” identified as MPG (miles per gallon) and provide conclusion based of the plots
2. Run a correlation analysis.
   1. Determine if any of the Correlation Coefficients are statistically significant.
   2. What is your evaluation of the strength and direction of each IV with the DV?
   3. what are your overall impressions after analyzing the correlation matrix?
3. setup and run the appropriate bivariate regression model and explain your rational

Interpret the results (based on the regression output).  

Temp	Humidity	MPG
27.0	18	8.4
28.0	68	10.7
32.5	59	12.4
39.0	69	12.8
45.9	35	9.4
57.8	10	9.9
58.1	33	10.8
62.5	74	12.5
88.5	34	14.4
49.0	57	10.8
45.9	18	9.4
17.0	46	8.4
48.0	55	11.7
32.5	68	11.4
31.5	58	15.2
88.5	24	14.9
25.9	65	9.4
45.9	15	12.4
32.5	59	12.4
39.0	69	12.8
45.9	35	9.4
49.0	57	10.8

Answer 1

a. b.

Corr( MPG, Temp) = 0.4795

Corr ( MPG, Humidity) = 0.2413

There is positive correlation for both independent varianle with dependent variable.

The test for significance of correlation,

H0: r= 0 vs Ha: r=\ 0

Test statistic, t = r*√(n-2) /√(1-r^)

P value for test of correlation coefficient between MPG and Temperature is 0.0239 < 0.05. Thus it may concluded at 5% los that correlation between MPG and Temp is significant.

P value for test of correlation coefficient between MPG and Humidity is 0.2793 > 0.05. Thus it may concluded at 5% los that correlation between MPg and humidity is not significant.

C.

The fitted model, y = 6.0406+ 0.0708x1+ 0.0460x2 explain 42.9% variation in MPG.

For unit increase in temperature, MPG increases by 0.0708 and for unit increase in humidity, MPG increases by 0.0490