Question

Marketing date on sales is presented for youtube. data are the advertising budget in thousands of dollars along with the sales. The experiment has been repeated 200 times with different budgets and the observed sales have been recorded. The simple linear regression model was fitted:

## 
## Call:
## lm(formula = sales ~ youtube, data = marketing)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -10.06  -2.35  -0.23   2.48   8.65 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.43911    0.54941    15.4   <2e-16 ***
## youtube      0.04754    0.00269    17.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.91 on 198 degrees of freedom
## Multiple R-squared:  0.612,  Adjusted R-squared:  0.61 
## F-statistic:  312 on 1 and 198 DF,  p-value: <2e-16

a) Calculate the Correlation coefficient r of the sales and youtube (respectively, y and x), SST, SSR, and SSE

b) Write the CI Formula and the number form for the slope coefficient.

c) Interpret the slope parameter

d) Write up the individual hypothesis test and its results for the slope parameter.

Answer 1

Solution:

Part A:

The value of Coefficient of Determination (R²) = 0.612

So, Correlation Coefficient (r) = 0.612^1/2

Or, r = 0.782

In order to calculate the SST, SSR, and SSE, we need the data set which is missing in the question...

Part B:

The formula for Confidence Interval is:

Here, the slope coefficient is 0.04754.

Part C and D:

Hypothesis:

H₀: β₁ = 0 (Null Hypothesis)

H_a: β₁ ≠ 0 (Alternate Hypothesis)

As the P value fro the slope of the variable "YouTube" is very small (2 * 10^-16), which is smaller than 0.05, here, the null hypothesis is rejected. The slope can't take the value of 0 as it is smaller than 0.05.

End of the Solution..