The following data represents the rate of return of the stock exchange (x) and t

Question

The following data represents the rate of return of the stock exchange (x) and the rate of return of a certain stock (y). The equation of the least squares regression line is y = 0.9764x+0.5975 and the standard error of the estimate is 2.3518. Answer parts (a)-(d). x | 0.23 0.94 1.40 3.86 3.25-2.53 1.89-191-201 3.00 0.90 y1.210.57 0.59 5.89 5.90 -2.58 0.06 1.78 0.06 5.791.57 (a) What is the mean rate of return for the stock if the rate of return of the S&P; 500 is 3.15%? y= 3.7 % (Round to one decimal place as needed.) (b) Construct a 90% confidence interval about the mean rate of return of y if x= 3.15% Lower Bound -D% Upper Bound (Round to one decimal place as needed.)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 0.5974944 + 0.97644807 x
Sample size: 11
R (correlation coefficient) = 0.69372156
R-sq = 0.4812496
Estimate of error standard deviation: 2.3517676

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

90% confidence interval will be:

Lower bound = -1.1 %

Upper bound = 8.40 %

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.5974944 0.76130489 0 9 0.78482932 0.4527 Slope 0.97644807 0.33792625 0 9 2.8895301 0.0179

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