Question

Solve.

a. When$x=1985,ŷ=\_\_\_\_\_$

b. When $x=1990,ŷ=\_\_\_\_\_$

c. When $x=1970,ŷ=\_\_\_\_\_\_$ Why doesn’t this answer make sense

Short answer

a). The value of$\hat{y}=2552$

b). The value of$\hat{y}=34275$

c). The value of$\hat{y}=-725$, The year $1970$not in the range.

Step-by-step solution

Part (a) Step 1: Given Information 

The linear equation is:

# AIDS cases diagnosed $=-3448225+1750$(year).

Part (a) Step 2: Explanation 

To find the value of $\hat{y}$:

$x=1985$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosed$=-3448225+1750$(year)

# AIDS cases diagnosed$=-3448225+1750\left(1985\right)$

$=2552$

Part (b) Step 1: Given Information 

The linear equation is:
# AIDS cases diagnosed$=-3448225+1750$(year).

Part (b) Step 2: Explanation 

To find the value of $\hat{y}$:

$x=1990$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosedlocalid="1649165820824" $=-3448225+1750$(year)

# AIDS cases diagnosedlocalid="1649165489151" $=-3448225+1750\left(1990\right)$

$=34275$

Part (c) Step 1: Given Information

The linear equation is :

# AIDS cases diagnosed$=-3448225+1750$(year).

Part (c) Step 2: Explanation 

To find the value of $\hat{y}$:

$x=1970$

Therefore, the linear equation will be written as shown below:

# AIDS cases diagnosedlocalid="1649165349688" $=-3448225+1750$(year)

# AIDS cases diagnosedlocalid="1649165322240" $=-3448225+1750\left(1970\right)$

$=-725$

It is known that the range of variable "year" is $1981-2002$. The year $1970$is not in the range.